I've been playing flats for most of my life - rounds early on, a few times used Pressure Wounds. My observations - at either end of the spectrum are Chromes and TI flats. I really don't care for the Chromes because of the high tension, and they sound too bright for my tastes. TI flats are very nice strings, but the very low tension only worked for me on a very limited application, fretless bass. I didn't like the feel of them at all on my P bass. My favorite flats are Pyramids, super smooth and great sounding once broken in (which can take a while). Like TI flats, they are quite expensive but last forever. If I were just looking to give flats a try, I'd probably go with LaBella 760FL strings. They're not very expensive, not high tension, and will give you a chance to see how you like flats. If you do decide to give flats a try, be patient - play the hell out of them for a month before you see if they work for you. Also flats shine best when played in a group setting. Pyramids don't sound that great when you are just playing by yourself, but in a group setting they really are perfect.
Good luck!