I've been to both and Bangkok would be my choice, but it's a personal one. I've always liked BKK and the Thai people. Yes it can be hot and sticky, but that's part of the place. Great hotels and great food and the place is manic. I have to admit it was a bit of a culture shock the first time I stepped out of the airport.

Been to both in July/August and going to both again next month. Both are fantastic places but Bangkok wins hands down. Both will have rain at that time. Hong Kong will have far more though. We have only been 5 days in Hk so my experience of the weather may not be typical. We had showers some days which were something else but they were quickly over! Bkk also has showers but not as bad- although we were there in a typhoon once! And that was an experience! It was the day we went to the famous Chatachuk market. Within half an hour the aisles were ankle deep in water( and its undercover!) . An hour later and it was up to our knees! Two hours later- it was as if it had never happened!
Hong Kong was a lot more humid than Bangkok. Great place though. Easy to get around and really friendly people. You can get a 5 star hotel in BKK for the cost of a 3 star in HKK. Its the only place we can afford to splash out on 5 star luxury! One thing I never got tired of in HKK - the skyline. It is breathtaking. When I was jetlagged and waking up feeling wide awake at 3am I used to just get up and sit and look out the window. Could spend hours doing that!
Hong Kong is easy to get around on your own- the MTR gets you anywhere within minutes. And if you just miss one you have to hang around for a whole 3 minutes till the next one. We found there was no need to do any organised tours. If you have 3 days in BKK however, I would suggest booking trips. Getting around is not quite as easy. My tip for a hotel- book one on the river so you can use river taxis or book one close to a skytrain stop. Our one- the Landmark- is right next to one.
I'm sure you will enjoy whichever one you decide upon.

I would also choose Bangkok, I think the Thai people make my choice, they seem much friendlier and warmer than the Hong Kong Chinese, both cities are loud and hectic. The heat and stickiness can get you down but always carry some water with you and don't let yourself get rushed. The hotels in Bangkok are on average cheaper with bigger rooms and allmost all have outdoor pools that are nice to cool down in at the end of some intense sightseeing.

Thanks everybody for your comments, they have really helped.

A bit of topic I know but I found my Chatachuk market typhoon photos. Have a look here at the first two. The taxi was just outside out the market. Remember that a couple of hours later everything was dry again!!