It's the lack of versatility. If you have the spells, you can load the exact same thing any sorcerer can, which is almost certainly going to be aimed at combat functionality. How many sorcerers are going to have a long repertoire of divination spells? Contact Other Plane is awesome, as is Legend Lore. As is Scry. Seems to me everyone talking about how people don't get why Sorcerers are good is simply asking some variation on "what if we dropped them both in an arena, who would win?". Which is one part of the game. But in a big campaign world, a well done one, not unlike the real world, it's about knowing what you are getting into first that allows you to bring the right tools to deal with it. Once all the research is done, then you can hat up and go in guns blazing.
But what about other spell combinations? I tried to make a single guy that could work his way through a deathtrap dungeon. He ended up being a necro with Investigation, Perception, Observant feat. He makes undead, sends them in to scout. Has them followed with an Arcane Eye. He has detect magic up. He sees what they see and what kills them. Assuming he's 15th level, he'd have Clone and Simulacrum, two spells I doubt any Sorcerer would ever get since they are so situational. But that means you have a duplicate of yourself at your side, who can at least blast away with cantrips forever, take hits for you, and assist on any skill checks(what an apprentice!). Also, if you die, you don't really die. You use those VERY specific spells, them put them aside for more practical ones until you need them again.
Teleportation circle? Any Sorcerer ever going to get that? Probably not. But a wizard would, and assuming you spend a few years in game time, you've got yourself a new network of rapid transit you made and you know about. A 15th caster also has access to 8th level spells. If that was me, I'd be using it to summon and bind elementals. Using a 6th level slot, you summon Invisible Stalkers. Use a 4th level slot make a circle that lasts 2 hours. Then use an 8th Planar Binding to enslave it for 6 months. Or even 1 month if you just want to use a 7th level. Even at 11th level you can use a 6th level slot to bind CR 5 elementals for a week. That's pretty nice. You'll have have a small army of loyal servants to carry out your business. Collect as many as you can or want given those constraints, then when it's game time you swap out to fireball, shield, whatever you want. You can have Dispel AND Counterspell. Also, you can use your divinations to increase the likelyhood you select the right spells for the job before you get to it. If you're smart. Do we need to see in the dark, do we need illusions? Wizards can do it all, and anyone who thinks that isn't amazing is nuts.
Anyways, you might notice I haven't even gotten to the specific type of wizard you are yet, because frankly just the ability to swap out spells and have access to ALL of them potentially, is awesome enough. The rest is just bonus. If you're looking for best in a fight, I'm pretty sure you're going with either Abjurer or Diviner, but any will do frankly. I would not play a sorcerer unless all I wanted to do was blow things up or had a DM that thinks that is all the game is about.
