With an integrated amplifier, you have pre-amp circuitry dealing with delicate low level signals coupled with hefty power amp circuitry, and a whacking great transformer. In a good amp, the negative effect of all this will be minimised, but to get the full benefit of both different sections of the amplifier, they're better off seperated in their own box with a power transformer that's designed and engineered to suit the individual needs of each section.
Pre/powers tend to give you a more accurate outlook on what's going on, mainly because the pre-amp isn't being affected by big power amp circuitry and transformers, and the power amplifier can be dedicated to just doing what it's supposed to do - drive speakers, and drive them well. Pwer amplifiers will normall be more powerful, providing higher SPL's and current levels - and damping factor
Whether you need to go as far as pre/powers is dependent on the speakers and their capabilities, but generally speaking most good quality speakers will always respond well to more capable amplification.
Having said that, there are some extremely capable integrated amplifiers out there - Naim's SuperNait, ATC's SIA2-150, and Bryston's B60. That's about as much as I'd spend on an integrated amplifier - they're all around £2,500. After that, I would always go down the pre/power route to get more from the system.
As for the tweaking, some will mix and match pre and powers to achieve their goals, but many will stick to one manufacturer to ensure compatibility.