I think it's fair to say it's time for Mr. Venator himself to weigh in on this conversation:
I recently read the novel Tarkin, and it really put the empire into perspective to me. Up until a point the fanbase believed that when the clone wars ended....the ships...the walkers...the guns...the tech all vanished overnight and the civil war era stuff appeared....but lets be real that's almost a 20 year gap between episode 3 and episode 4.
So Tarkin essentially puts a realistic spin on things....the Empire is not all end all be all...new tech rains from the heavens...there is a gradual build up and retooling. Remember here that there were THOUSANDS of Venators and Acclimators built for the war....throw in a few hundred thousand V-wings....Arcs....whatever. Now you suddenly win a war and you have to hold that territory you just subjugated by force.
TL/DR: Venators and the like served in the empire for a long time following the end of the war...the empire needed ships and they were provided.
Now if anything, it's obvious the Venator will see use with the Empire...it's an Imperial ship. It's a dedicated starfighter carrier...and oddly enough I could see it being refitted to carrying ties rather easily. Acclimators probably along a similar vein...sure they aren't the most up to date...but they are there, sturdy, reliable, and can do the job as dictated. It's only when you really piss off the empire is when the ISD's show up.
It's pretty clear they would keep the capital ships and refit them for newer starfighters...their mentality is numbers...period...and gutting a Venator's flight deck to have it carry a few hundred ties and then sending it off to patrol is easier (and more cost effective) than to send an ISD 2 that costs much more...and might be needed elsewhere.
Now the starfighters are a different story, they are sturdy and reliable....and expensive to run...which flies in the face of the empire's doctrine of numbers numbers numbers. Arc 170's and V-wings probably ended up in the hands of the Rebels.
Capital ship wise...the rebels would get their hands on the mid sized droid cruisers. The Luce's most likely not....it's too big to crew and use effectively. It flies in the face of their early doctrine, hit and fade. It's easier to get your hands on and crew a smaller, more nimble droid cruiser and fit it with some crew spaces for a living crew (with a fraction of the crew cost) and roll from there.
Droid fighters....I'd say no period...the empire probably figured out a way to shut them down/jam their signals.