I'm a fan of both rounds and flats for different reasons. There is no rule of thumb, though certain basses do shine better with certain strings. But first off let's dispel the myth that rounds "cut through the mix better". Depends on your definition, but brightness and treble do not automatically equate to cutting through better. They may offer you the brighter top end and lower end punchiness, but it's those mid frequencies that get you slicing through a mix. Thus, a bass with scooped mids that's all treble and thundering lows won't get you through a wall of overdriven guitars, though if the guitars are the carrying the majority of mid range frequencies then having the bass EQ'ed over and under it can give you a huge overall sound covering the full range. Again, not "cutting through", but rather, filling out the overall frequency ranges to create an overall wall of sound. But, I would argue that flats can cut through a band mix better because, and this really depends on what bass you're using them on, they offer you a the right thump/attack and mid frequency bump. (Precisions were MADE for flats, IMO. The perfect blend of low mid bump and thump). Slapping/popping, without question, I'd use rounds, though there's no rule of thumb and you can slap on flats too. (Larry Graham, anyone?). Just a different tone. And that's also not to say a bass strung with rounds couldn't be EQ'ed to achieve similar mid bump results, and likewise a bass with flats could be EQ'ed with the mids scooped out as well. Check out early Joe Jackson records or even the first Dead Kennedys record to hear how trebly, bright, and aggressive flats can sound, for example. As for string noise, I generally find flats more forgiving, though, again, depending on how you choose to EQ your sound, you can certainly dial in any amount of ugly, clickity clackity, fret/string noise you want in combo with your bass's setup/action and EQ. (Steve Harris has made this part of his sound with his flat strung P).
I guess I haven't really answered your questions.
Bottom line: determine what you want to do, try each, and especially try them with the rest of your band/musical endeavor, since you should be focusing on the overall band sound and not how great your bass sounds at home solo'ed.