Why do you use flats verses round wound or visa versa?
How long does a typical set last?
Whats the lonest you went before changing?  
Do flats last longer that round wound?
What about the sound of flats verses round wound?
Lets hear all comments!

Generally, flats don't sound as bright as roundwounds. They don't have that zing that new roundwounds do, but you also get much less finger-squeak. Some flats are brighter than others - D'Addario Chromes have a reputation for being pretty bright when new.  
 
A lot of the modern bass sounds - Stanley Clarke, Marcus Miller, Chris Squire, Geddy Lee, John Entwistle (the originator of rounds for bass!) - are very bright and require rounds, and I think that's what many of us are used to. Flats are a different sound altogether. Actually, Steve Harris of Iron Maiden uses flats, which always surprised me, because his sound has a lot of treble click but he also changes them every show! Phil Lesh used flats in the early days of the Grateful Dead, which also surprised me, but it makes sense considering he was co-inhabiting a musical space that included two guitars and keyboards. I think the classic flatwound sound would be Duck Dunn, James Jamerson, etc.
 
Just some rambling, hope it helps!

I'm a roundwound player in general...like the sound and feel better.  Counterintuitively, I find that the flatwounds can hurt the fingers after playing for a while.  Maybe just a difference in callus formation, though.

i like halfwounds...

I always use roundwounds live because they cut through the mix better. In the studio I sometimes use flatwounds in order to get less noise, finger squeaks, etc. It depends on the song and what the band, artist or producer are looking for.

Strings are realy pretty personal...To me ears roundwounds, especially on an alembic are a little too bright for me, but flats sound awesome.  Only way I can describe it is as a   nice, dry woody sound.

yeah, i think when you play flatwound on an alembic, its the perfect sound, the sound of the alembic is pretty bright, and playing flatwounds, you get more of a distinct bass tone, without sound too crazy on the bright side.

I used to play steel rounds in the old days, but I like the Chromes these days.  Reasonably bright on an Alembic without a lot of string noise.  You have to have great technique to play really bright strings on an Alembic.

TI Flats on my bass, they last me about two years, I do wipe them down after sessions.  as stated, a nice dry woody tone, no growl, no finger noise.

Stainless steel roundwounds are very bright, almost Hohner Clavinet sound when slapped and popped BUT the are very abrasive to the frets.
I have used flats when playing a lot of jazz, to get the big double bass sound along with an octivider and defret options on the pedalboard.

Stainless steel roundwounds are my favorites,they bring out that alembic Bell or that Bling Bling sound in my Bass!.......i also love flat wounds for that vintage Motown sound.

I like compressed roundwounds

Neither set of string can produce the same sound, so IMHO any bassist worth his/her salt should have a bass with flats and stainless/nickel wound strings on them. Flats also give you that Jamerson, McCartney, John Paul Jones sound and who would'nt dig that?  
A set of flats usually last about a year for me (simply because I break the damn things)as opposed to my regular round wounds which I change every 3-4 shows(simply because I break the damn things if don't change them!).

I agree Adam, use 'em both, how else could you pepper you show with differents timbres.
 
OO
PS. I used to regulary break strings too when I was still gigging.

+2 on basses strung with both!
 
Here are a couple of soundclips of my Fender Telecaster Bass equipped with Alembic Activators and new D'Addario Chromes. The first clip is played with fingers (it's a demo, ignore the clunkers!), and the second is slapped with the frequency full open.
 
rays of sound (fingerstyle)
 
8B4X4 (slapped)
 
(Here's a thread with pictures, etc.: Telembic Bass. Plus, the soundclips are pretty low-volume, and the bass will sound better on headphones or decent speakers)