FrogReaver
The most respectful and polite poster ever
So, a player asked me today in what way is a Wizard at all better than a Sorcerer. Since we are just beginning 5E, I have one player as a Sorcerer, but no one has played a Wizard yet. In looking over the classes, all I could suggest was the larger spell list for the Wizard. Any other big ticket things I am missing???
To more directly answer this question, no matter what options the sorcerer chooses, Wizards are flat out better than sorcerers at:
exploration
debuffing
providing a safe place to rest
(Provided an appropriate wizard subclass) Staying Alive
(Provided an appropriate wizard subclass) Using illusion spells
(Provided an appropriate wizard subclass) Using enchantment spells
(Provided an appropriate wizard subclass) Using divination spells
(Provided an appropriate wizard subclass) Raising undead
(Provided an appropriate wizard subclass) Dispel and Counterspell
Wizards are quite a bitter better than a sorcerer at some relatively broad areas of the game while also being better than the sorcerer at some specific areas of the game provided an appropriate subclass. That's the answer to your opening question.
The larger spell list isn't what they are better at than sorcerers but that larger spell list and their greater number of spells known and prepared and their ritual casting allow nearly any given wizard to excel over any given sorcerer in the areas I listed above.
The only things a sorcerer can do that is better than a wizard is buff and it requires one specific choice at level 3 to make that possible. Sorcerers also can slightly edge out evocation wizards on blasting IMO but it's not enough that it makes giving up the other wizard advantages worth taking sorcerer over wizard for this IMO.
So I guess really the question that should be being asked by your player is, what can sorcerers do that wizards can't?