I can't make up my mind either. Have to get one or the other. Here is my perspective on things, as I first posted in the Desire HD vs iPhone 4 thread:
SGS wins over DHD on:
- Super AMOLED screen (no need to say more)
- Gorilla Glas protects the screen
- Batterylife (SGS is almost on par with iPhone 4, and the DHD have a smaller battery, and the talktime and standby time according to htc.com is a lot less than that of the SGS).
- Camera performance (according to GSMarena it beats iPhone 4)
- It comes preloaded with swype. I would just looooooove to swype

- 119 gram vs 164 gram of the DHD
- SGS is big but slim. DHD might be just a tad too big.
DHD wins over Galaxy S:
- Better build quality (no plastic)
- Generally more pretty
- HTC Sense owns Touchwiz 3.0
- Locations (preloaded maps etc.)
- HTCsense.com
- It might be bigger in the pocket, but the screen is bigger to look at

- Dual LED flash for those rare but critical "a bad picture is better than no picture"-situations
There are a lot of differences between these two phones, but the above mentioned ones is the ones I say make a difference for me.
I do not take into consideration the bugs with the SGS lag and its GPS problems, because I expect those to be fixed, and also its getting the Froyo before I need to purchase (Am getting the phone 1st of January, but have to decide/order now, its a company phone).
I tend to lean towards the DHD, but batterylife is a big showstopper for me, if it can't last a full day, without me worrying wether it will die on me or not.
EDIT: Added the dual LED flash as an DHD advantage, atharh convinced me

EDIT2: Removed DLNA as SGS also has it (I wasn't aware until now)