I was wondering this myself a couple of weeks ago when planning our trip. If you do some searching in the recent pages of posts or even do an advanced search about each hotel you'll find lots of comments about both hotels and it should help you a lot.
We orginally were going to "go big" and do GCH, but after reading these helpful posts, I think it comes down to what you are looking for, versus which is "better." Ultimately we chose the DLH, but are going big there and doing the conciege level to get the most out of it, because we're going with our five-year-old and it sounds more like a kid and Disneyesque hotel than the GCH, which is more traditional and beautiful and nice, etc etc etc. Plus we're always of the mindset of going at the highest level possible in the category of hotel we can afford versus getting the worst room at the best place...(our concierge level room at DLH is cheaper than the basic view room we could have got for a comparable price at GCH!)
Outside of the style, each hotel has different pros and cons: room size, access to the parks esp DCA, location in general within the resort, pools, age of the hotel, I could go on from what I've read...I'm sure some folks will still write into your message and give you their thots but in the meantime check out what's already available to you, it sure helped me!
Good luck deciding, that's part of the fun!
Good luck!