My current PCs are in two different campaigns: Ea is a Tiefling Monk with anger issues, Taka is a Halfling Rogue with a bad gambling habit and too much pride to admit it.

Ea would probably be indifferent, trying to ignore Taka.
Taka would do a bunch of annoying things to try to rile Ea up.

If Ea's in a good mood (or slightly intoxicated) she might make jokes about their height difference (She's 6'2" while Taka's only 3'4").
If Taka's in a good mood/slightly intoxicated, she'd probably try to teach Ea a bunch of naughty words in Halfling.

They'd probably not work well together, since Ea is trying to find a "true religion" and Taka's trying to pay off a bunch of debt (see: gambling habit). Ea would be annoyed at the seeming greediness of the Halfling while Taka would see visits to temples, cloisters, convents and the like as time-consuming and pointless, especially with armed debt collectors on her trail.

They'd probably become the living embodiment of the phrase "Fight me" as a pair.