Yeah, I forgot to mention that as I was just thinking about the spell slot table. However, you're right—Arcane Recovery gives them effectively more spell slots. I should add the proviso that the sorcerer's Flexible Casting allows them to trade Sorcery Points to spell slots and vice versa (though, using Sorcery Points this way gives you less to use on Metamagic or subclass-specific abilities that are powered by Sorcery Points that compete for usage).Not really. Well, technically they have the same number of slots, but in practice arcane recovery means wizards get more slots if they take a short rest, and sorcerers get less spells overall because metamagic eats away sorcery points if not slots themselves.
You heard it right, Wizards cast more spells than sorcerers.