Yes, 5E Fireball is a bit unreal at either 14 or 28 average damage, but then again, a 5E 5th level fighter gets 3 or more attacks, often hitting and often doing 30 points in a single round.
The caparison was between the same class from 4e to 5e, not between 5e classes. You asserted that 5e wizards did less damage than in 4e. Relative to monster, hps, we can now agree, they do more.
One aspect of 5E casters though is that they really do not have more spells per level. Even if they go offensive with every single spell at level 5, that's 10 to 12 non-cantrip offensive spells and a boatload of cantrips.
In a 'typical' 5e day of 4 or so 4-round encounters thats 12 spells and 4 cantrips.
In 5 encounters, 4E wizards get 10 encounter, 2 daily and 1 utility spell plus their at wills
4-5 encounters is more typical of 4e, and rounds are likely closer to 5+ rounds than 3 or 4. So, two full-on spells, 2 lesser encounter spells used 1/encounter each, and 10 uses of at-wills. Also consider the variety of spells. At the start of the first combat, the 4e wizard has offensive options. That drops to 4 once he's used up his dailies. Each encounter gets used once, so if you assume using encounters early in every fight, choices are 6, 5, 4...until he finally uses dailies and ends 3, 2. The 5e wizard preps 9 spells plus 2 cantrips for 11 choices, assuming he is as reluctant to use his top-level slots as the 4e wizard is to use his dailies, he retains those 11 choices until he has used up his highest-level slots. But, really, 11 understates it, since the wizard can choose to use lower-level spells in higher level slots. So, for instance, each scalable level 1 spell represents 3 choices for the 5th level wizard. If those 9 prepped spells are evenly distributed over the 3 levels of spells available, that's 20 choices total, including cantrips. Dropping to 11 when out of 3rd level slots, and 5 when out of 2nd level slots.
5E casters do have more flexibility, but then again, many of the 4E powers do more than just damage.
As do 5e spells. 4e powers are more likely (for the wizard, almost certain) to do both a some damage and an effect of some kind. 5e spells are likely to do significantly more damage relative to enemy's hps /or/ much more dramatic effects.
At level 20, it's 22 to 32 Dailies for the 5E caster, and in 4E, 29 encounter, dailies, and utility powers in 5 encounters (not including bonus stuff from feats, themes, items, etc.).
Actually, it's 4 encounters, 4 dailies, 2 at wills, and some utilities, but why not cut to the chase and compare level 20 5e to level 30 4e. Then you're talking 2 at-wills, 4 encounters, 4 dailies and 6 utilities - plus (probably) an epic power of some sort, for a total of 17 choices, declining to 13 in each fight as encounter powers are expended, and to 9 as dailies are expended. Compared to 25 prepped spells, plus 5 cantrips, for a total of 30, dropping only when that top-level slot is expended, and not including the choice of casting scaling spells at various levels, which could easily push the total over 100.
And 4e was supposed to inflict decision paralysis.
Neo-vancian needs something to offset it. Easily saved spells, even for high level on and fewer of them (and wimpier in some cases, stronger in other, but not by too much).
Actually, saves may end up tougher than they've ever been outside of optimized 3e builds. Save DCs scale with 1 stat, easily pushed to 20, and automatically scale with proficiency. Prettymuch from 13 to 19 over 20 levels. Save bonuses, OTOH, scale with six different stats and only two receive proficiency. That means a caster will always be able to target a non-proficient save with no more than a +5 bonus - and possibly with a much lower bonus, even at high level. For a rare save, like CHA or INT, the worst case could easily be a -1 save penalty trying to hit a DC 19. In contrast, in AD&D old-school Vancian, save 'DCs' only went down as the targets leveled up, the caster's level and stats didn't come into it. A few spells would give a -2 save penalty (or even as much as a -6 vs specific targets or in specific situations - though the only example I can think of is Feeblemind used against another caster), but save bonuses could be accumulated from all sorts of items, as well as getting into the very low single-digits at high level. Failing saves only on a 1 was common at high level. Fighters, in particularly, improved /all/ their saves very quickly as they leveled.
So, yes, neo-Vancian gives fewer slots, scales with slots instead of levels, and has (for now) an arguably less-problematic set of spell lists. But saves are definitely looking pretty good from the caster side, relative to old-school Vancian, or even 4e attack rolls. Even relative to 3.5, save DCs scaling with level instead of slot is on the win side for 5e casters.
