Both Dinobot and Rattrap are capable of forming a strong meaningful romantic relationship with a femme. This is true of most people, no matter how irritable they seem (like Dinobot) or how superficial they portray themselves as (like Rattrap). You'd have to be really far gone to be totally incapable of succeeding in love.
The question is, would they have similar tastes in love?
I'm going to say yes.
Why not? Alright, they wouldn't look in the same places for her. Rattrap would look in bars and clubs, casually dating and secretly wondering whether it could turn into something more. Dinobot...wouldn't look at all until it hit him. Probably another warrior.
But both would admire bravery and adherence to some kind of code. Yeah, Rattrap seems slack and lazy but he's not stupid. He doesn't really shirk his duties (though he complains a lot). He would hate amoral people. Of course, if this femme was to speechify a lot about honour that might bore him.
As for looks, if she fit in with Rattrap's definition of hot, that'd make it easier for him to like her. But why assume Dinobot wouldn't go for hot as well? Just because he doesn't talk about it doesn't mean he'd turn his nose at it.
A nice bright good looking femme with honour and who knows how to have fun, who can kick skidplate on the battlefield and isn't naive. Why wouldn't Dinobot or Rattrap like her?
EDIT: I didn't read the part about sharing a femme. Nah, they wouldn't. Unless, like Sinead said, Rattrap was messing with Dinobot.