I like flats, but have never been able to make them work well in the rock bands that I've played in, they tend to disappear more in the mix. But I do have a Pbass strung with flats and in the right mix they work great. I play flats at church and they work well but it's a much less aggressive music and more acoustic sound. Not saying you can't make them work, especially with a pick, but rounds at least in my experience are much easier to work with and cut through much easier.
Rounds are more flexible in terms of what they are capable of, so if I were you I'd stick with them.
Good luck with the "hit you with a pillow" thing. You get that from recordings and car stereo, sub woofers etc, but going after that doesn't usually work very well live unless you have the big bucks sound system and someone who knows how to mix it. Wait until you play with someone who wants to crank the subs and you'll understand what I mean.
Flats are great, but from what you write, I'd stick with rounds. Just get a good basic nickel round like a DR Sunbeam and have at it.