I'm moving out for a year, but when I get back I'm considering buying an acoustic-electric bass guitar. I'm curious as to their versatility in general.
I play a lot of jazz (and other genres) and in my mind, the acoustic will be better at mimicking the sound of an acoustic upright bass than the sounds I'll be able to get from a solid body. At the same time I want an output so that if I want to do some "more different" stuff, I have that option available as well.
What do you guys think on this? Am I better served finding a nice semi-hollow body electric or something? I'm curious what the best options are.

I bought a good friend a second hand acoustic bass guitar about 7 years ago or something, for his birthday. He has a Fender Jazz, and Stingray. The first thing he did was send it into a shop to get the action sorted, which made me realise how much he valued it, to invest in it. I went back in August and it was stood in his front room with the others. He says he plays it plenty and has done a few session jobs with it too. I'm can't recall if I knew when I bought it, but I was surprised that the frets were marked, but weren't actually frets. meaning it gave him a even different sound than he has as both his electrics are fretted. He's a big Jaco fan too.
 
I understand fret noise is a big issue, but some like that character, but if you were looking to replicate an upright more, then maybe fretless is worth considering and they could be marked to help the transition.
 
I like the sound of an acoustic, noticed a while back that Sigur Ros sometimes use one, and just yesterday was listening to the Alice in Chains unplugged session, they used an Acoustic too.

I have a Fender "T-Bucket" bass. It's acoustic with piezo pickup system. I will say it's very versatile and gives some unique sounds I can't get out of the P Bass. Since it's not fretless it doesn't have a full uprite sound and feel but it is very cool and I can take it to a camp fire.
 
I only spent $400 for the bass and it was worth every penny. I only wish that there was a better selection of strings because I can only find round wound and like flats.

Some are OK, some are pretty poor. Much depends on the setup and fretting job just like any other guitar.

For amplified use piezo pickups can be very harsh and brittle sounding unless it's a good pickup and connected to a good preamp. String noise and squeals when moving around the fingerboard can be an issue, especially of the piezo is naturally bright-sounding.

If you want to use one acoustically, the guitar sized bodies mostly aren't really big enough to produce low frequencies (compare one to a cello or upright bass) or much volume. Basically acoustic bass guitars are like acoustic ordinary guitars, you tend to get what you've paid for.

Something I like about acoustics over electrics, is that I am more likely to pick up an acoustic randomly and practice, but then my amps are software amps.

I haven't played it myself yet, but I have a friend who jams with a guy with a Guild a/e Bass. I've heard it, and it sounds amazing.
 
Here's a great, recent video of an audio test of a Guild acoustic bass. Enjoy!
 
https://www.youtube.com/watch?v=sReVucg7zy8
 
Edit: The one I heard was an older, all-mahagony fretless Guild.

Personally I've never liked them. At all.
 
Obviously many others disagree.

I think if you want to sound like an upright, you should just buy an upright, and a clip-on mic.

Or rent Tony Levin. 

craigb
Or rent Tony Levin. 

Nah, he'll just stick it to ya.