It's not the same class at all... but as you say, Arleigh Burke-class is the same class as Fletcher-class.
Old hardware will and have to be replaced after some time. The Sentinel class and Lambda class is very old ships
The shuttle Kylo ren is using is the Upsilon class, a totally different vessel then
http://starwars.wikia.com/wiki/Upsilon- ... nd_shuttle
While Darth vader used the Lambda class. Upsilon replaced the Lambda.
http://starwars.wikia.com/wiki/Lambda-c ... 4a_shuttle
The other vessel you see in Star Wars 7 is the Atmospheric Assault Lander
http://starwars.wikia.com/wiki/Atmosphe ... ult_Lander
Lambda and Sentinel class was designed and build during the war. war ended just after the "last" original movie (SW6), Star Wars 7 is placed 30 years after Star Wars 6, I estimate the Lambda and the Sentinel class to be more than 50 years old. So replacement for them is obvious.
The X-wing you see the rebels use in Star Wars 7 is the same X-wing from Star Wars 6, the history behind the small changed on it, like for example the engine, is that they wanted it to look like the Rebels couldn't afford new equipment, so they had to modifie existing equipment.