Other cabs will definetly sound different, the question is if you'll be more happy with it.
I had the 1960 A first - and didn't like it too much. It was an old one from the JCM800 era.
I later got the 1960AV and my guess it sounds a lot like your cab. I must say other cabs sound fuller and better. I was in the fortunate position to compare it on the spot to a 1960A and a Mesa/Boogie Rectifier cab. The Mesa has a bigger and fuller-bodied sound and works great with lower-tunings (I tried my baritone gutiar with it :-) !)
The thing is, I'd still always choose the 1960AV because it just cuts through the mix so much. It also sounds very aggressive and ballsy, I always think of Schenker and Angus Young when I plug my Marshall into it.
So if you're happy with your cab I don't think you should really change that.