We've done 11 cruises with
DCL, 3 with Celebrity, 2 with RCCL, 1 with Azamara and NCL. We just came back from a 14-nights Baltic on Celebrity Silhouette. We sailed in a Celebrity suite (with a private butler, private gastronomic restaurant, unlimited drinks, unlimited internet, etc.) and the cost per night was 100 $ over what DCL was asking for a regular verandah room for a 7-nights Baltic cruise. It becomes more and more difficult, in our view, to justify the DCL cost on European cruises like the Med or the Baltic. That being said, we are booked on a Magic cruise for next year in Europe...
The service on Celebrity, in public spaces like restaurants, bars, guests services, etc. is as good, and sometimes better, as what we receive on DCL, and much better than what we perceived on NCL, even sailing in Haven. Our stateroom attendants have always been as good as on DCL also, whatever category cabin we've had. The dinner buffet is spectacular, so much so that we often found ourselves hesitating between it and Luminae. The breakfast and lunch buffet are better than Cabanas, but not by much.
DCL offers better shows, a much better kids program - our son refused to go to the Celebrity kids club after the open house - and much better onboard activities. Most 'activities' on Celebrity involve you getting a sales pitch. There is a casino, art auctions, plenty of luxury stores and the necessary advertisements for all of them, but you can easily ignore them.
European cruises are very port-intensive. DCL offers better tours geared towards kids than Celebrity, but if your family looks forward to visiting historical sites or beach breaks, it will not make a big difference. Of course, the crowd on Celebrity is much older, so tours are adjusted to that fact.
We would never hesitate to sail Celebrity in Europe, in any category stateroom. Outside of the kids clubs and some oboard activities on sea days, we don't find ourselves missing DCL.