I don't know how the separate units work, other than a gas heater will heat a pool faster than a heat pump.
With the heat pump I was trying to heat on weekends, but figured out it works much better, and is much more practical to set the temperature and have it maintain. The warmer the water is the more efficient the heat pump runs, so when the water cools all the way down it takes a lot to get it back up again. Also, I resisted a solar cover for a long time because I hate them, but finally gave in because it cuts the overnight heat loss in half (and therefore the heat pump's power bill in half). The pump runs about 7500 watts of power use, and heats about a degree an hour, and ran 2 to 3 hours a day during the extended season. So if you know your power cost per kwh, you can figure that out.
This was our first year with it, and I did not need to run the chiller except to test it out, and it seems to cool the water coming out the returns considerably. We had a good 30 day stretch of 100+ degree days this year, but not the 110+ stretches we usually get, so our water stayed pretty comfortable without the chiller. So for us, given the not so often need for a chiller, I would not have bothered getting one standalone, but the small cost difference of a heat pump vs a combined unit made it make sense.
Our electricity is expensive but we have a good sized solar power system on the house.
