These are two of the most popular and smallest DSLR stabilizers. I'm not going to say one is better than the other when it comes down to the actual video footage. End results between these two micro flyers would be the same once you have them fine tuned and balanced. The main differences to consider between these two is cost, quality of build, time to balance, and handling.
First no surprise here, the Flycam Nano can come in about three times cheaper than the Glidecam HD1000. The Flycam Nano comes in a bit smaller than the Glidecam but this also means it won't handle as much weight. If you want to stick to the smallest flyer but are concerned you might be pushing the limits too much, then the HD1000 might be the safer bet. The Flycam being the smaller stabilizer can pack down smaller for traveling. Of course the Flycam Nano can easily handle a 7D + Tokina 11-16mm (and then some), which is about the average weight needed for most entry level flyers. The Flycam might be a better choice for smaller cameras like the Sony SLT-A55 or Panasonic GH2.
The Flycam build quality isn't as polished as the Glidecam. Cheaper materials, painted metal instead of anodized plating, lack of fine tuning knobs, tiny handle, and non-professional looking weights. That's what helps keep the cost down. The Glidecam is far superior in build quality, but fancy plating alone doesn't make it a better flyer.
The Glidecam handle is much larger and more comfortable to grip. The Glidecam handle is the same width as it's larger HD2000 and HD4000 siblings making it possible to use the HD1000 with a full Vest. The Flycam has a much smaller and shorter handle designed to be used with an optional Flycam Arm Brace.
The Glidecam HD series stabilizers also have fine tune knobs. The fine tuning knobs allows micro movements of the stage making exact placement of the camera much easier and faster to the center of balance. This is a great feature for anyone who seems to change out lenses, cameras, or accessories that require the entire stabilizer to be rebalanced. If you're pretty much set with the camera + lens combination for flying, a Flycam Nano with a quick release adapter should do the trick. No need to rebalance.
Here's a sample video with the Glidecam HD1000: http://cheesycam.com/glidecam-hd1000-dslr-video-stabilizer-demonstration/
Here's a sample with the Flycam Nano: http://cheesycam.com/flycam-nano-stabilizer-abused-with-7d-tokina/
Glidecam HD1000 Video Camera Stabilizer