Wow, my mistake, I completely forgot about the two automatic spells a wizard learns each time he gains a level. I need to stop posting when I'm half asleep.
Yes they do make a lot of difference
I can't really say much about how other DMs make scrolls available to Wizards for copying. It can be anything from "none" to "every spell in the book" and I just can't provide any statistics.
But as a matter of fact even if you consider the
worst case for the Wizard, i.e. having only the spells known when levelling up, the Wizard still has more known spells than the Sorcerer (except one cantrip).
But that's not even the true comparison... that's merely a
formal comparison of the variable we call "known spells".
A better
substantial comparison takes into account the fact that even the number of
prepared spells by the Wizard is bigger than the
known spells by the Sorcerer. These are really what matter on an adventuring day.
With these in mind, you can see that the Wizard is someone who (even in the worst case) has
each day available for casting more spells than a Sorcerer, can change the list every day, and has even more available as rituals (the Sorcerer cannot even cast Rituals!).
And the difference between Arcane Recovery and extra slots by Spell Points is numerically very small. Just do the math! The Sorcerer's advantage here is rather in the fact that Arcane Recovery is very "stiffy" (you can only do it once a day, needs a short rest, and can only recover slots you've actually already spent).
This is just to say that the 2 most common praises on Sorcerers are
blatantly wrong:
- "Sorcerers cast much more spells than Wizards"
- "Sorcerers have an advantage in not needing to prepare spells beforehand"
They were true in 3e, but plain false in 5e, apparently because people haven't yet seen many groups with a Wizard and a Sorcerer simultaneouly.