Why does everyone here think sorcerers can cast more spells than a wizard of the same level?
Let's look at a 3rd level casters.
sorcerer can cast NO 2nd level spells, the wizard can cast 1 + 1 for school.
let's look at a 4th levels.
sorcerers can cast 3 2nd levels and the wizard can cast 2+1 for school The same number of spells.
And to top it off, the wizard knows a lot more spells,
Why does everyone here think sorcerers can cast more spells than a wizard of the same level? . . .
Who says that?
Yes, sorcerers tend to have more slots, but it's pretty close, usually. For wizards, there is little reason to Not specialize in pathfinder, so add one to any total on the chart. (Given the chance I'd add two with a Thassilonian Specialist Wizard [Greed/Transmutation or Sloth/Conjuration], but that's just me...)
Also, wizards get scribe scroll starting out, so they should be making a few utility scrolls for when they don't want to use a slot or after they've already run out of slots for the day. Sorcerers Can do the same thing, but they'd have to invest. All characters need to plan ahead, but wizards tend to gain more from it than others do.
Another reason why a sorcerer can cast more spells is they have the flexibility to use higher level spells to cast lower level spells. A wizard who has cast all his memorized magic missiles encounters a shadow and has no other force spells can’t really do anything. The sorcerer on the other hand can still cast magic missile even if they have used all their 1st level spell slots. It may be a waste to use a higher level spell to cast a lower level spell, but it is better than dying because you can’t do anything.