Specifically UR decks, both the aggro, tempo, and control variants.
UR delver is weak to chalice on one but runs more than enough basics to ignore our 8 moon effects. We don't really have a lot of effective sideboard options to replace moon post board either. Post board they side in usually 3 smash to smithereens. Basically it's the same difficulty we have against burn compounded by the fact that they have a robust countermagic suite.
UR tempo is similar except they play more 2-3 drops making it easier to play around chalice, and 4 snapcaster which post-board lets them get a lot more value out of their artifact destruction, making bridge and chalice less useful. Same problem of them running more than enough basics to virtually ignore moon.
I also saw a few experimental UR "control" lists running punishing fire and grove of the burnwillows without green cards, using it just to power punishing fire. A few others were running lists similar to responsiblejoseph's tempo list but without the tempo cards, focusing on landing blood moon, jace, and true-name, and protecting them with countermagic, burn, and snapcaster. I also saw several maindeck engineered explosives in these lists, presumably to kill chalice, which worked well against me.
Anyway back to my original point, all these decks are pretty hard for any stompy variant to deal with, but I've had the easiest time with the bridge/walker version because it's threats are better at eating red spells, at least trading for 2 of them in most cases. Moggcatcher just kept dying too easily.
@jandax, Grixis is a great matchup, I'm more than happy to play against any deck that doesn't run a single basic any day.