We are Platinum on DCL, and took our first Celebrity (X) cruise to Alaska last summer - and really enjoyed it! Celebrity has similar service and ship size/capacity to Disney, but at a better price, and with a lot more variety in itineraries. We're sailing them again this summer. Even our teenager enjoys Celebrity. It's a different sort of cruise for us - but given we're looking for specific itineraries and planning to maximize our port time, it's perfect as we don't feel like we have to run back to the ship for fear of missing out on activities (which we often do with Disney).
X offers both fixed and anytime dining options, but each ship also has more than one added fee dining location (signature restaurants). These are clearly marked in their Daily (Navigator), so you shouldn't have unexpected expenses. They do have free hand-dipped ice cream in the buffet, and for-fee gelato near Cafe Al Bacio (Cove Cafe - but with more/better pastries). They do offer packages for multiple signature meals. They also offer drink packages as soda isn't included (except in the dining room, I think) - both alcoholic and non-alcoholic. You can often get that included in your fair on a promo.
Celebrity's cabin categories are basically the same as Disney (what confuses me the most is the deck names vs. numbers - it's a little harder to figure out where cabins are in relation to the Promenade or Lido decks without knowing what numbers they are), and the classes within those categories are similar - higher price near the center of the ship. Room numbers don't always follow deck numbers, so that can be confusing as well. Our daughter slept on a pull-out chair (not a couch) on the Millenium, but it looks like she should have a couch on our Reflection cruise. If it's just the two of you, you can book in Aqua - those rooms all sleep 2 only, but have some added amenities, and a dedicated dining room (Blu) as well as access to the Persian Gardens, which has heated tile loungers and aromatherapy rooms.
X does have an adults-only area (the Solarium) with a pool and spas - though on some itineraries (Alaska), they do have family hours in the indoor pool. There's also a spa and gym on the ship. The premium coffee location (Cafe Al Bacio) is not in the adult-only area. The buffet is open pretty much all day (6am-2am), with some down time between meals - but there's something available at least, as well as tea and coffee pretty much whenever. Since the buffet is open for dinner, we typically end up there as we can eat what we want when we want. They do tend to have themed meals in the buffet on different days, as well as having standard fare (pasta, pizza) and cooked-to-order options (omelets/eggs in the morning, meats/fish in the afternoon/evening). There is a pool-side grill as well, but most of the pool deck food is easily accessible in the buffet.
Shows on Celebrity aren't quite in the same league - they do have comedians and such like Disney, but their stage shows aren't quite the same thing. They're enjoyable, but we never felt that we needed to see them (while we rarely miss DCL shows, unless we're on B2B cruises). In Alaska, they had someone on board who gave great talks on nature and science - more educational than trying to sell something. DCL does similar things with local port expert talks, so very similar there. X also offers line dancing classes, a lot of trivia, karaoke, some craft events, etc. We didn't do many of those, though we did enjoy watching some of them (especially trivia) from the Sky Lounge, which is right over the bridge with amazing views.
One big difference is shopping - X has a mini high-end mall in their ships, while DCL has a few shops. They do have a Celebrity shop on the X ships, but the merchandise is minimal. They focus more on their high-end stores selling watches, jewelry, and high-end fashion. They do offer daily specials in the center, with some interesting and often local-themed specials which can be a good deal.
One thing to look at on X is the current available promos. It's pretty easy to amass a fair amount of OBC on X with promos and deals. I think we had over $600 on our first cruise, and $500 on this cruise. Previously you had to wait until you were on board to use OBC - unlike DCL, where you can pre-book dining and excursions, and it doesn't get charged until the event on-ship, X requires pre-payment for anything booked before the cruise. However, they recently started allowing you to use your OBC to pre-book excursions and beverage/dining packages. It only applies for OBC from Celebrity itself, so if your TA offers some directly, you will only be able to use that on the ship - but it does make it easier to book some of those ship excursions you want to make sure you get if necessary!
While we love DCL (and do have another DCL trip booked), we really enjoyed X and will be sailing with them more in the future. It's a different type of vacation - which isn't a bad thing! We did find it more relaxing overall than our typical DCL cruises (which always feel like go-go-go, and you still miss something), but does miss that extra bit of magic that is Disney. However, the cruise staff was just as helpful and the service was great, and once you get over the fact that you don't enter into the atrium with your name announced (though they do hand you a glass of sparkling wine), there are no characters wandering around, and you can't find hidden Mickeys allover the ship, it's easy to settle in and feel welcome and comfortable.