Maritan, If you went to tube amps, it would be best for two channel music only. They wouldn't match very well with solid state, in a home theater system. And, an all tube theater system costs a fortune. You would need all the speakers to be tube powered. Also, tube amps like efficient speakers in general. Speakers that run around 8 ohms, and fairly efficient, meaning they don't need that much power to play loud enough.
Some people switch between a tube amp for the front two main speakers, and then switch back to the solid state for home theater. That gets to be a pain though, and risky. A tube amp needs a speaker load on it whenever it's on. So if you accidently switch a tube amp on, with no speakers, there a risk of ruining the output transformers. That gets costly.
I'm guessing there must be solid state amps out there that would do better. A lot depends on your speakers, and other gear too. If your speakers are good at revealing things, a better amp may work. The Integra's preamp section may limit it some too. Also, if your speakers like a lot of power, or are 4 ohms, an outboard amp may make a difference for that reason. A lot depends on your gear you have, and what your looking for.