There are a few but none of them are significant except maybe earthquake.
The few spells more known have the potential to be useful, but are very rarely crucial. It's often like carrying around tools in a tool box that never get used hoping to use them someday. It's pretty hard not to find a use for meta-magic.
The actual gap in spells prepped vs known is actually rather small until high levels. It only works out to about 1 additional spell per spell level prepped over known. Wizards still run into "I wish had had this spell" moments. I've seen people post like they are simply prepared for everything but that simply isn't true. More spells prepped is certainly useful but I find it's been over-rated.
I largely agree with this, except wizards tend to prioritize combat or utility spells before selecting rituals because of the opportunity cost in the selection. At least I did and those whom I gamed with did. No one ever selected all rituals, lol, although I do definitely select rituals on wizards and bards.
It also gets to Mistwell's comment I'm including below.
The wizard's method of acquiring rituals is far better that the feat. Tome warlock's have the same issue. Gaining rituals because of the feat isn't as rare as you are making out unless the DM isn't using published adventures and is willfully not including them in his or her campaign, which would be odd unless the campaign has no NPC wizards.
The wizard method is better. ;-)
What you stated is mathematically impossible because knowing 44 spells in a spell book cannot allow for swapping out the entire spells prepared in a day. Signature spells at 20th level precludes ever swapping out the entire list and it takes 50+ spells in the spell book to completely swap out the other 25; not that I've ever seen anyone ever coming close to trying something like that or giving a reasonable explanation on how that many spells swapped would be relevant. ;-)
Clerics obviously cannot either because a huge portion of their prepped spells if fixed by domain. The same goes for paladins. Non-land druids are the only class that can really swap out the entire list and it's still mostly pointless, although I think they might have the best argument for the relevance because of the focus on nature spells when in a non-natural environment.
It's not going to change the specific power level in any given spell by swapping it out. A 7th level spell is just as powerful as a different 7th level spell, in theory at least. Swapping spells is a versatility boost but not a power boost, and even as a versatility boost it's not common. Most wizards carry their favorites and swap in what they think they might need but it's not much of a swap. The actual number of spells prepped versus known is more significant than the ability to swap them out.
In any case of spells known being swapped or cast, they are still the same spell levels of slots being used for similar levels of power and restricting the addition spells known to an opportunity cost in actually casting them. IE, a slot used for a wizard spell the wizard has prepped is a slot no longer available for use later regardless of the number of spells prepped, and isn't inherently more powerful than the same spell slot a sorcerer uses for a different spell. Meta-magic is what makes spells more powerful using the same slot.
Not swapping spells is less of a restriction on using spells effectively so much as precluding niche use spells because of the need to select spells that cover general use. Then they take wish at 17th level to cover it all if needed anyway. ;-)
The 15 spells is a bit restrictive but all it means is covering the needs with general use spells, and possibly relying on gear and equipment or ability checks / skills. Spell selection needs to be more thought out but it's not that difficult.
"Casting Time: 1 reaction, which you take
when you see a creature within 60 feet of you casting a spell"
If the caster doesn't see the spell casting (because no VS components) it cannot be countered. There's a few ways like that to avoid counter spell. Subtle spell can also help if the party is trying to be stealthy if they are within earshot of monsters, during social encounters, or when bound and gagged. It's not as flashy as twin, quicken, or heighten but it's got it's perks.
As to the topic, I prefer sorcerers to wizards these days. Playing a wizard often felt like I was packing around a toolbox full of tools that I wasn't using in case I needed them. That's great when a person needs them but it wasn't prominent enough to matter as much as meta-magic does. I'm good with a better basic hammer instead of 3 different hammers, so to speak. ;-)
The extra spells prepped is nice to have but it's not the end-all / be-all people make it out to be sometimes. The same goes for rituals, which can be picked up via feat but even then it's nice to have but not that important in the long run. More spells prepped I might use << meta-magic that I will use because the spells are situational and might not matter in the slightest. Meta-magic is deliberate and something I know I will always use.
I made a chart with typical spells known in standard options.
View attachment 113853
The wizard, cleric, and druid can vary with caster stat choice and is assumed 16 with 18 at 4th level and 20 at 8th level. The same is true for the paladin but they can be a bit MAD and it's assumed 16 then 18 at 12th level and 20 at 16th level. Warlock includes arcanum with the spells known in parentheses. None include subclass bonuses with the obvious exception of EK/AT.
It's important to keep in mind that the warlock spells known are split among 5 instead of 9 spell levels so the representation per level is consistent with other spell casters. It's also important to note that warlocks can easily pick up more spells known via invocations so between spells known in lower levels, arcanum known, and invocations picked up they do fall within the same main pack we see.
Paladins have a lot of spells prepped and all of them are in the 1st through 5th level, giving them a better representation than every class other than clerics and land druids in those lower levels spells. I'll point out that having a lot of spell prep obviously doesn't place them on a spell casting level of full casters to demonstrate that having a lot of spells known isn't indicative of more or better power in itself.
On a similar note to warlocks we have rangers, eldritch knights, and arcane tricksters splitting up their spells known among lower levels. This is the big drawback for sorcerers because they have more spells known than these three options but having to split them up over twice as many levels is what stretches sorcerers as thin as rangers. I've seen house rules that simply continue on the level progression (level +1) or adds CHA mod to spells known. Those don't actually break anything (spell slots available is the true bottleneck) if a DM wants to give a bit more variety to sorcs but they are house rules.
Side note: There was a game reasoning behind it. Sorcerers are considered more self-taught / naturals instead of educated, which is why they don't have a lot of spells or ritual casting by default. Wizards come from academies, bards from colleges, clerics from theological institutions (churches or temples usually), and druids from circles. They are "educated" and hence ritual casting and more spells available. An educated sorcerer subclass would be consistent to add spells known and possibly ritual casting as a feature if you want to work with your DM on it.
From what we see in that chart above bards get 2 bonus spells known over sorcerers at 1st level and that's about it until the high tier, and wizards and druids have a similar benefit of only a few spells (2-3 until almost high tier). Warlocks have nearly identical progression outside of the potential of a couple of invocations until the high tier. That demonstrates the gap in spells known / prepped isn't that significant regardless of class compared to sorcerers until high tier. The key difference is the high tier spells known, which is limited with sorcerers and warlocks (getting back to the side note on "educated" spell casters). Given that the bulk of spells is still going to be cast through lower level slots instead of higher level slots (again, slots are the bottleneck) this still isn't as big a gap as it first appears.
Sorcerers have enough spells between spell levels to cover the basic needs of the class, and cantrip spamming or damage is prominent among several of these classes in which warlocks and sorcerers tend to have the better options (EB invocations and meta-magic) in all tiers.
FWIW, I prefer the meta-magic. I only need low, medium, and high level spells for attack, defense, and some utility. 2 attack and defense (or CC) spells each of low, medium, or high level takes 6 spells known and the rest I can do with whatever. Wizard utility is very over-rated, IME. However, it is nice to have more spells available and easy ritual access. The grass is greener whichever a person prefers. ;-)
The general rule is that wizards, bards, clerics, and druids are schooled by institution of some form and have more spells available (particularly demonstrated with high level spells) plus rituals while sorcerers and warlocks are more hedge casters but have the better options to directly manipulate the spells they have. Hopefully that helps. If you go wizards, which sounds like your preference, my vote would be diviner. That's my favorite wizard subclass.
There isn't actually a wrong answer on what to play. The only difference is how the player sees what he or she is playing. ;-)