If you can do a couple of days in Singapore, then get an air asia or similar airline to HK for 3 nights, then also have a night in Macau as well. That would be a good trip. 6 days in either place is boredom, as you run out of things to do.
HK is quite good, 6 days you've probably seen most things close to the city but venture further into China and it is totally different. As suggested, trying to do the 2 would be great.
There are more things to do in and around Hong Kong. Singapore is very clean, if that is your thing, with a few things to see but more than a few days as a tourist is enough.
Loads of stuff to do in HK outside of the immediate hustle and bustle. Most people don't know about it or don't have enough time. Get out to the coastal parts for some great walks, country parks, beaches etc.