Live I run from the onboard pre-amp through a 7-band EQ which helps with room-specific feedback issues, and straight into the board. I was using a Behringer DI-20 until we filled our board with other stuff, now I just go straight 1/4" line in because that's the only channel I have left . Sometimes I will use a Chorus as well, but not often.
On larger stages I may use my Washburn acoustic amp just for a little more warmth and stage monitoring. I accomplish this by using the 2 channel DI which can split the input to send one signal to the amp and one to the board for the PA.
At home I rarely amp-up when playing acoustic, but might use either the Washburn or my little Peavey 4 channel PA.
My acoustic amp has a mic input as well, so it is handy and portable for those occasions when you just want to jam or do a little semi-unplugged set at a birthday party, family get together or some such. Would also work for a coffeehouse type gig and a smaller church setting.
I notice a huge difference when playing through an acoustic amp or PA. Electric guitar amps just aren't designed to reproduce the "depth" of an acoustic. To me they sound really "tight", which is what you want with an electric. Acoustics should sing through a wide range, from full (but not boomy) bass to crystal clear highs. You probably wouldn't notice a big difference at bedroom volumes as you are still getting some of the actual "acoustic" sound from the guitar itself, but crank 'er up so the amplified sound is louder than the instrument itself and you'll see what I mean.
Good luck with the search.