In a head-to-head comparison of these two, Bi-Rite wins. Both take pains to create a certain atmosphere, with descriptions of philosophy and provenance of ingredients. Ici is perhaps a bit more Martha Stewart Provencal, but there are two other significant differences. One is in the attitude of the staff. At Ici, they seemed miffed at having to come out from behind the high counter to deal with the lineup (besides us, mostly mommies and nannies with very small children) and were focussing on "processing" us. At Bi-Rite, they let us take our time, even when the shop was crowded, and kept offering unsolicited tastes and chatting about whatever took their fancy.
But the acid test is the ice cream itself, and in this respect Bi-Rite comes out ahead again. Their salted caramel and roasted banana flavours are great, but so were most of the other ones we tried -- the exception being soy chocolate, which my older daughter ordered for some inexplicable reason. (I know, it's not ice cream, but I've had Tofutti, and this is much worse.) Bi-Rite's flavours have a suitable intensity and balance, not feeling overly rich. Ici's flavours are more muted, and even the most successful of them -- on the day we visited, lemon-pistachio and honey-basil -- seem like they're riding on top of the same substrate, relying on luxurious mouthfeel to do the work.
This is probably good, because Bi-Rite is harder to get to for us, but a better alternative to the caloric mace-to-the-head of Tartine, once we're there. I just hope that success doesn't make them cocky. --PR