I can address this from personal experience...
The lines vary in accommodation. This seems mostly because of the crew and how attentive they are. We found many kind crew members more than happy to assist on the Celebrity Reflection and others who appeared indifferent and clueless on the RC Serenade of the Sea until we filed a lengthy complaint mid-cruise.
MDR seating has been a big problem but we eat early and usually don't have any problem identifying a table for two close to the entrance. The buffet area is problematic because of the lack of trays now. I have to get Dave's meal, then find a seat, and then go back for my own. By the time I get back to the table, Dave is done eating. There are not enough handicapped tables and tables that are easy to get to tend to get gobbled up by able-bodied passengers. One thing we experienced on the Serenade was that people tended to just sit for extended periods of time in the buffet... well after finishing their meals. This made finding a table to sit at and eat next to impossible for most of that voyage.
As for the theatre, we notice more rows reserved for handicapped passengers but these are usually the last row of the theatre so sight lines to the stage are not the greatest.
As for getting on and off the ship, we have used a personal scooter for the last two cruises but after Lufthansa destroyed my husband's new Tzora scooter we hesitate bringing it on another trip (they paid for the repair and also replaced a brand new Briggs & Riley bag damaged on the same trip). However, we did see escorts providing wheelchair assistance on both of our recent voyages. The downside is that you have to wait for the escort service to retrieve you. That can be trouble if you have tight turnarounds for flights.
One of the big problem areas is on excursions. No matter how hard we tried to reserve motor coach seating, other passengers who consider themselves as handicapped see the reserved marker and assume the seat is for anyone who is handicapped and they feel entitled to sit there no matter how much the tour guide tried to reason with them that the seat was specially reserved for someone. We have asked that our cabin number or last name be put on the seat markers.. that seems to help but it should not be something we have to stress over time and time again.
Quite honestly, the biggest problem we experience since my husband's illness is that of rude and inconsiderate fellow passengers who also seem to go out of their way to be nasty or to make things just a little bit harder for us (e.g., not holding the elevator door for a few seconds long enough for us, rushing up from behind us to get into MDR line ahead of us)... and the crew simply can't be held responsible for that. That is common courtesy and situational awareness that cannot be taught.