We have sailed both quite a lot. You enroll in Celebrity Captain's Club and your D+ on RCCL will get you Elite (not E+) on Celebrity. But you need to call them to do this.
The Celebrity ships have no equivalent to the RCCL Diamond Lounge. They instead have drinks available to you at any bar on the ship at the designated Happy Hour times. Limited drink menu.
Internet- two types. Elite get a certain number of minutes or you can buy a package. If you do the Celebrity "Always Included" package you get a number of things included like basic unlimited WiFi. Look it up to see what is included for your package. Usually a drink package too.
A Jr Suite on RCCL is the entry level suite but you pretty much get nothing with it. On Celebrity the Sky Suite is the entry level suite and it has access to The Retreat, Luminae (suite restaurant) and usually OBC, Premium Bev package, Wifi, and paid gratuities, and a butler. Both the Jr Suite and the Sky Suite are typically 1.5 cabins in size. The Concierge Class on Celebrity is not a suite but a regular veranda cabin on S-Class. Not much extra.