Of course that had to be Cunard and the QM2 as she is a liner rather than a cruise Ship. She is built for that north Atlantic crossing from S/Hampton to NY.
There are many Cruise lines moving their Ships from the US to Europe for the summer months. More and more ships are targeted for the European Market.
I read the other day from Celebrity that they and RCC will have 11 Ships deployed to Europe.
Every Cruise Line has these crossing so you need to decide what sort of cruise you want depending on how casual or formal you want it to be. Always lots of good offers out there for Spring March/April/May and again Oct/Nov/Dec for the return crossings.
I have only ever done Spring Crossing in the South Atlantic but have made 2 North Atlantic crossing on the QM2 in July.
Everyone will have their own idea but perhaps you will be led by price etc.
Hopefully others will give you more advice on this.

Sue

Depends what you are looking for from your cruise ship you spend a lot of time on the ship

Tell us more about what you like to do.
Different ships attract a very different mix of passengers.
Different lines have different stuff that is free.

Also think about itinerary can often be easier to go from/to the Med flying if you are a long way from UK ports.

EU->US you gain 5 hours so get long days, short days the other way

On a TA the cruise directors team can make a massive difference
lounge entertainmnet can also be more important.

The large RCI ships are good loads to do and lots of space but no covered pools
The promenade is a great feature.

Celebrity Millenium class have a great thallasotherapy covered pool and better food overall than RCI.
tends to be a bit more dressy (casual is ok though)

NCL freestyle and loads of choice for eating.
Also NCL has the best suite perks and on a TA you get max use of these.
Check out the Courtyard villa or the garden villa(sleeps 8 )

QM2 mainly does 6/7 night crossings so no good if you want a 2 week trip.

As windjammer says it depends on what you personally want from a cruise.

I mostly do 2 transatlaantic cruises a year but add on time in the US either before the cruise or after I love the seas days and now having seen most of the places in the Med am very content to just cruise plus love being in America with just 1 long flight last November we added on a 5 day cruise from Miami it worked well with the timing and cheaper than a hotel on south beach

I like Celebrity,RCI,Princess but the QM2 is my favourite they will defer your flight home and you could add some time on in New York

Windjammer is right about the large RCI ships but Jewel & Brilliance are great for the crossing with the indoor pool area