To add to Gerry's answer (and this will be slightly too long for a comment), there is a huge disadvantage to drastically changing the cockpit when going from an A320 to the A320 NEO or from a B737-300 to the B737-700, or 737 NG to 737 Max, and that has to do with the existing fleets.
If you keep the cockpit basically the same and just add what new switches are needed for the new engines, then most if not all operators can qualify their pilots in both models, and integrate the new arrivals into the fleet with minimal disruption. Need to substitute a NEO for a standard 320? No big deal, the same crew can fly either one. If the cockpits are wildly different, then the new jet is essentially a different type rating, and the pilots will have to be qualified (Edit: "qualified" in the airline sense -- current & qualified, not just type-rated) in one or the other, but not both at the same time. So when you substitute an aircraft, you have to change out the crew as well. That adds up to a lot of overhead, training costs, and scheduling inefficiencies.
In the case of the A-350, it IS a whole new aircraft, and nobody would be qualified in it at the same time as the A-330 or A-320, so there's no great need for backward compatibility. But in the case of the A-320 NEO, keeping commonality with the existing A-320 fleet so that pilots aren't restricted to one or the other is a big deal.
Now, I can just hear the objections... you said "B737-300 to B737-700 -- that's steam gauges to glass!" Yeah, sort of. BUT: Boeing "dumbed down" the 737 NG cockpit tremendously compared to what it could have been so that operators of the 737 classics could keep their pilots qualified on both the classic and the NG simultaneously. There was the "6-pack under glass" option for the NG displays, which made the NG display look like round dials, so that pilots used to the Classics had reasonably similar displays when they flew the NG. Less noticeable but still important, the overhead panel and the automation of the NG's was kept essentially the same as the classics, even though advances in automation would have enabled a FAR more modern approach to nearly every system in the aircraft and their management.
The option to digitally display round dials -- source page.
Another image -- showing how even the engine instruments were not much more than digital depictions of the round dials:
Consider: the 737 NG is a more recent design than the 777, but the 777 aircraft in 1996 had automation light years beyond what even the 737 Max rolling out this year has. The overhead in the Max looks essentially identical to the overhead in the NG, very very close to the overhead in the Classic, and not dramatically different from the overhead panel of the 737-200 from the late 1960's! Why? So that airlines never had to segment their crews.
If the 737 Max were being rolled out "in a vacuum" today, its cockpit would look a lot more like the 787's -- which was mostly a "clean sheet" design (some commonality with the 777 flight deck). As was the A-350 -- clean sheet of paper. But the B-737 Max and the A-320 NEO aren't "clean sheet" designs and keep significant commonality with their predecessors, because that's what the airlines insist on.
For better or for worse.