BA can bring Assault units with FnP, Death Company IS devastating. The get access to a highly mobile and survivable flyer-unit wich can deliver a assualt unit and a dread to almost any place. They have fast transport (inkl. fanzy discounts), can drop raiders, have preds, that can shoot all weapons on the run. And i am sure i miss someting else. Terminators with FNP in Raiders for example.
Otherwise you can spam jumppacks to overload the enemy an then get into it.
But: Rhinos are meh, even if the are fast, dreads are meh only 3 HPs, vulnarabel to meltabombs/grenades, jumptroops are meh (they die like servos without jumppacks), death guys are meh, because they are so expensiv with packs ....
If you want, you can run your BA very assaulty. Soften up that orkmob, vindcate thet bossmob (you have 30" vindies) and assualt the rest, flame that eldars and bolter them befor you hammer-of-wrath-them.
In 5th BA have their hightime, but they were played shooty as hell, never assualt-oriented. No it the shooty editon but they can aussault too and have the right tools.