Another vote for the non-stop. You'll get the same miles with a stop as the non-stop unless you actually break the flight up and continue on with a different flight. If it's the same flight, no extra miles. Not that the extra miles would amount to much anyways.

Traditionally, the stop in HKG was on a A330, which is the least desirable if flying in C. The older birds have the old regional style seats and the new planes have the new seats but with ridiculously limited recline. So neither are very good. Recently though they swap the planes out continuously and it's a total crap shoot as to what plane you'll get. Still though the HKG route seems to be more likely to get an A330. HKG though does have a nice TG lounge to use during the stopover, not far from the TG gates.

Doing a stopover in TPE, forget it! This is the worst option, being as already mentioned the gate waiting area is horrible. TPE in general is horrible. TG's lounge is landside, and so anyone transiting cannot even use it. It might be possible to use SQ's lounge (I did it once), but it's a very long way from the TG gate and you'll only have at most 5 minutes in the lounge and have to practically run both ways. Meaning it's of zero value.

Forget about the two meals you'll get if you do a stop. It's not worth it. Whenever I've done the flight with a stop I only choose one of the segments for a meal and try to sleep through the other segment. Unless you're a really big eater, one meal is plenty.

The above advice is strictly if you don't care about the timing of the flights. For me the timing is normally paramount, so except for morning flights from ICN to BKK where you can choose a non-stop or a stop, there's really no choice.