Well, as it is I don't know what the stats are for a sorcerer at either CR3 or CR4, so the question whether CR3 or CR4 would be better is somewhat moot. Would you use the stats on the table in the DMG on page 274 for a sorcerer?
My main problem is that I get the feeling that if I make two characters which are identical in everything except their selection of spells, I would end up with different CRs. What CR is a level 5 sorcerer with Fireball compared to one who has Stinking Cloud instead?

@Tobold Pretty sure that's exactly what Imaculata meant, it's just his first sentence was a typo.
You're right in your calculations for the most part, and the selection of spells can affect CR. Certainly a sorcerer with fireball is more dangerous than a sorcerer with some noncombat spell like water breathing. But blink and stinking cloud are very much combat spells. They make the sorcerer considerably harder to kill. To do them justice, they ought to be factored into his defensive CR. And estimating how much damage they prevent -- how many hit points they're effectively worth -- can be a bit of a judgment call. Just to ballpark it, I'd start by assuming that they prevent roughly half the attacks against him and so count similar to resistances. But they're more conditional, so maybe reduce that effective value by half.If I changed the level 3 spells to Fireball and Lightning Bolt, the sorcerer would deal an average damage over the first three turns of (84 + 56 + 27)/3 = 56 damage, for an offensive CR of 7 (after adjustment downwards for the low spell save DC), overall CR of 4. So I do think that the selection of spells does affect CR.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.