feet, definitely. i actually have it written down as about 1000 meters. the TH being just under 14K ft. and the summit 16,800 or so.
a few things-
we arranged a ride from a friend in quito, early AM- 2 hour drive to TH, we did the RT and he drove us back for about $70. i can't speak for his availability, he was happy to help. the day before we climbed rucu pichincha, right outside of quito, now accessible by a gondola for about $7 to 13,900, then hike/scramble to the 15,400 ft. summit- great for acclimatizing. an easy cab ride from your hotel/hostal.
you can arrange a ride in a camioneta from latacunga or machachi including a return and stay at either of those places- might not find more than a two door pickup, tight for a group, especially if its raining. those are easier places to get going on your next goal like cotopaxi than is el chaupi.
2 years ago we bused to machachi(1 hour) then bus to el chaupi, near the TH and stayed at a hostal, the only one there, owned by an ecuadorian named vladamir. he also owns the hut at the illinizas and can drive you the remaining miles to the TH and pick you up, as well as pack your gear up to the hut on a mule if you like. he runs everything up there, his hostal in chaupi is real nice(unlike the hut) and will do meals for you as well, none of it too expensive. he can also shuttle you to and from el corazon(acclimatizing peak) if you like. he got us a ride to the cotopaxi hut the nextday.
lots of guide groups like to sleep up at the hut, but in tents, there's plenty of space. they get the time up high but don't have to stay in the hut. for a few bucks you can use the kitchen in there so you don't have to pack fuel. we stayed in the hut, we should have camped outside.
one way isn't better than the other. the day trip is nice, but if you need the extra time up high then i would use the mules to haul up your camp gear and you can spend 2 nights. besides, the hostal is nice and sometimes traveling on the buses adds something to the trip.
we did a fair amount of acclimatizing around here(aspen) before. after the day on rucu, we did the RT in 6 hours- 4 up and 2 down(2 to the hut). it helped that i had been there before so there wasn't much for routefinding on the upper parts of the route. also, there is an express descent down sand/gravel/scree right below the summit pitch that gets you down quick w/o having to repeat the upper scrambling- definitely makes it faster only it connects youwith the trail well BELOW the hut, about the halfway point from the TH to the hut. so if you're staying there you need to climb back up. not a huge deal.
if you were considering illiniza sur you wold have to stay at the hut, that's more than a day trip