I picked the DLH studio. We stayed in the DVC Discovery Tower last year (albeit in a 1 bedroom), and even though it was a bit further than GCH we really loved everything about it. The bright colors, the theming, the brand new everything, proximity to Trader Sam's and the new Palm Breeze bar.
Later that year we also stayed at GCH (we always book standard there), and while I still love the location for proximity, I found myself missing DLH. For one, the grounds of DLH just feel more relaxing to me. The lobby at GCH is always so packed and feels even chaotic at times. The rooms are also starting to show their wear, some pretty badly. I can see why they are doing the refurbs soon...it's needed! And that aspect also scares me, like gottalovepluto mentioned -- I tend to avoid hotels during huge projects, and the concierge lounge expansion sounds like a doozy (along with room refreshes). But I will say that Disney does a great job of trying to minimize guest impact, so I don't think it will be off the walls awful.
I hope you have a great time whatever you decide!