Hi, I don't think you can go all that wrong with either But as a proud owner of a Beco Butterfly v.1 and a Beco 4th Gen, and ex-owner of a Connecta, I thought I shoud chip in.
I didn't get on with the Connecta because I didn't realise it was supposed to be worn 'apron'. DD loved it though. The only reason I wouldn't try again (properly, this time ) is that I have RSI and found the buckles a bit stiff and spindley. Not in an 'unsafe' way but in a 'have to squeeze harder than is comfortable' way. As this was with an as-new Connecta and the Becos I've tried had more use, that could be the true reason! They seem really popular so this can't be a common problem.
I love the Beco 4th Gen (but I suspect you mean a Butterfly). Padded waist and body, and it uses the same buckles as an Ergo, which means that you can extend it with the Ergo waist extension. I don't think the body is as tall as the Connecta and I found the detachable sleephood a nuisance. Doesn't pack very small.
The Butterfly is great for someone like me who isn't the very best or most confident with back carries. But a lot of people find it digs under teh arms and is a nuisance to strap the child into. Many people find that a Calyx does a better job of the same. (I'm one of the unusual people who prefers Beco Butterfly over Calyx!)
Also, the Butterfly isn't great if you're the sort of person who likes to do crossed back straps for front carries. It's more of a rucked straps job, as I think a Patapum or Ergo is (someone who knows more about these may be able to enlighten). Also, I found the child harness on the butterfly a real hindrance for BF, though I'm not sure you'd absolutely have to have it between you and the LO. So I'd say it's great for someone who isn't confident with back carries, but not such a good all-round carrier.
Of course, it could be different for a Butterfly v. 2 - I've only tried v. 1. I think the only differences are that v. 2 has longer straps and a removable newborn insert.
Sorry, that's turned into a bit of an essay! I think most people would send you to a Connecta and I'm the odd one out. Yes, what browny said, defo come back and tell us what you went for!