Both, and it does not seem to add that much expense. I've insulated half the flues on this old house, using both insulated (wood appliances) and un-insulated (oil appliances), but always being different lengths and conditions (thimbles, etc.), it's hard to compare price directly:
44' un-insulated 6" rigid tube with cap and collar, and thimble to basement oil furnace: $1300 in 2001
22' un-insulated 6" flex with cap and collar, and thimble to basement oil furnace: $1795 in 2011 (actually I paid less than this, that was the higher of the two quotes I received, can't remember the amount I actually paid)
23' insulated 6" smooth-wall flex with block-off plate for wood stove on 50' high, steep, standing-seam metal roof with enormous flag-stone chimney top in the way: $2400 in 2011
13' insulated 6" smooth-wall flex for woodstove, slid into existing 8" round clay tile, reusing existing block-off plate and cap, $1100 in 2011
The smooth-wall flex was a $200 - $250 mark-up above standard flex (installer quoted both ways), but I never asked the price difference to do the wood appliances with un-insulated. I knew I wanted insulation to help with my draft on the 13' flue, and to avoid creosote build-up in the 23' flue.