Game Center Live the quality is slightly better. 4000kbps vs 3200kbps at hockey streams.
Hockey Streams low end option is only 800kbps, where as judging by the VLC links that leak, Game Center has multiple different tiers such as 1600kbps, 3200kbps, 4000, etc. Meaning, if you have a sketchy connection, and intend to watch live, Game Center seems like the way to go.
You can watch Hockey Streams using VLC, so Flash isn't as much of an issue.
There's a legal grey area with both, because you'll need to use a VPN or some sort of spoof for Game Center, and Hockey Streams is not a licensed NHL service. So it's up to you to decide whether you're comfortable with circumventing blackouts, or supporting Hockey Streams service.
Hockey Streams gives you a lot more content. They stream every North American league. Olympics. Often they stream non-hockey sporting events if they are big deals.
If you are technically illiterate, but can handle setting up a VPN, I'd go with Game Center, only because there are a lot of times I've had to trouble shoot with hockey streams. Simple things like browser compatibility, or on demand streams randomly restarting when I try to skip forward. Not big deals, but it does end up being less plug and play.
Another thing is, Game Center seems to have an APP For everything. Apple TV, PS3, etc. So if you don't have a HTPC, or don't like using your laptops HDMI output, Game Center is more universal.