From what I can tell, the two planes are very different. Grot bomms are a serious threat to planes, as well as ground targets. You'd need to use at least two grot bombs to take out even a single objective (they seem to have 3hp so if two bomms hit one will usually do extra damage), though the cool thing is you could do it from pretty far away, beyond AA range and they can't be shot down on the way. So actually, that sounds pretty good. On the other hand it has awful flying stats and barely any firepower except to the front, so enemy fighters (or at least those that survive the bombs) will take it to bits.
Eavy bommers instead have quite a lot of all-round firepower and some bombs. I wonder though if you would be better off to just field a load of fighta bommers instead. These can take the same number of wing bombs but are also reasonably good fighters. That said, an eavy bommer is twice as tough and not a whole lot more expensive, and it can throw a lot of bullets in most directions. It looks very vulnerable to things like thunderbolts tailing it at medium range though.
Finally both have transport capacity, and grot bommers seem like pretty good transports. The grot bomms will make life a bit awkward for enemy fighters and they can do a bit of strafing themselves on the way in - since even they won't be outmanoeuvred by a static ground defence. Eavy bommers have transport 2, but since they're less effective at fighting against planes and worse transports, I think you leave them at home in these missions.
From what I've read people seem to field a lot of grot bommers and few eavies, if any. That makes sense to me.