HKIS is about 50% American judging from a recent International Day event, but there are students from 20-30 countries there. My own son's class is probably only about 35% Americans. The teachers are primarily NOT Americans, with a wide spread of UK, Aussie, Canadians, NZ, Japanese, American, etc. You do have a religious component to the school, but this year my son learned about Islam and Hindu religions. Really not a big deal for us.
In my son's class (R2) I'd say about 50% of the kids are "South Siders" meaning for those who live over the mountain it's a bit tricky to get down to the birthdays and after school activities. Still on our road in Midlevels there are about probably a half dozen kids in his age group.
The first few years are built around "learning through play". I don't think there is any homework assigned until second grade. That sometimes freaks out those parents who are like 'study-study-study now-now-now!'. The secondary school has a slightly more academic reputation than the primary school.
For us it was a matter of liking HKIS more than GSIS (we found their administrators a bit overly cocky, the lack of Mandarin annoying, and didn't really like their kindergarden/lower primary facility out by Cyberport). HKIS also put our son in the "native stream" for Mandarin education (as compared to the 'as a foreign language' stream) whereas GSIS wouldn't offer Mandarin until grade 6 or so.
It's worth noting that both schools have redevelopment plans in the works. HKIS is going to move their lower primary kids probably in the next year or so to a temporary facility, and I think GSIS has a upper primary or middle school move to a temporary facility planned (or underway). Depends on your kids' ages of course, but check with the school.
Basically though, you won't make a wrong decision going to either place.