Been there, done that, with horrible results.
There are two situations here.
You are playing with PA support with subs and you don't mind getting a weak (no lows) reference sound at the stage, the audience gets the punch, and you can play comfortably with that reference sound, then go for the powered speaker setup.
You are playing in a place where the lows come from the backline, in this situation you are doomed.
I can not speak for all the "full range" PA style powered speakers in the market but IME, those kind of speakers are not designed for the kind of lows output that a bass needs, some are better than others at filling the room, sometimes you will get a decent result in small rooms but the results at most places will be lacking.
For your reference, playing a fender P/J jazz through an SVT emulation with the lows at 50%, sometimes playing standard E, sometimes detuning with hipshot xtender to Low B.
It lacks/farts with most powered cabs.
You have to look for a powered bass cab which is transparent enough and has enough frecuency range.
Roland makes a powered satellite cab with a 15" + tweeter IIRC 300 watts, then you have the bergantino powered series and Markbass is preparing something with Alain Caron, a powered markbass cab. which I am sure will be quite flat sounding (for a bass cab) and as lightweight as it is possible.
Hope it helps.
