Something that's occurred to me is that the d20 character creation system is very tied into action sequences. Feats do things like give you extra movement or attack options. Your BAB and hit points go up with level. That kind of thing. The Chaosium BRP Call of Cthulhu, on the other hand, is all about a very granular skill list. Your stats are generated at character creation and never change, but your skills go up in very tiny increments over time.
Honestly, I find myself torn between them. On the one hand, I really like the customization of talents and feats afforded by d20 — but on the other hand, in a mystery/horror context, how useful is Power Attack really, y'know what I mean? Besides, in CoC scenarios as written, half the time character sheets are superfluous anyway. If the characters go to the library / dig into the newspaper archives / interview the witnesses, they are pretty much going to find out what they need, and if they don't, they don't.
This issue is going to take some more thinking. I don't really like the BRP CoC mechanics. The skill resolution is simple enough, but most of the time the character's stats don't actually seem to matter that much except when it comes to "resistance rolls," which require a bit more math than is handy. It's not hard math — the formula boils down to (10 + your stat - the opposed stat)x5 or less on percentile dice — but it's a bit awkward to do in the middle of a heated moment. You could simplify it by taking out the "x5" and changing it to a d20. But even then, your stats are more or less divorced from your skills. It doesn't matter if your DEX is 8 or 18, your Sneak skill is still going to be 10 + however many points you put into it. The rules in general seem to be kind of slapdash, with a lot of arbitrary "roll under POWx3" here and "roll over DEX x 2" there. d20, for all its focus on combat, is a much more coherent system overall.