"Advanced audio quantize" vs. hitpoints, audiowarp, etc.

There are many different ways to shift timing of audio in CB6. There is “advanced audio quantize”, hitpoints, audio warp, “define track tempo”, etc.

I am having trouble understanding WHEN to use a certain tool for a given purpose - and how to use it properly.

For example, I have a hip hop vocal that I wanted to tightened up with respect to the instrument track. I thought this would be easy using “Advanced Audio Quantize” but it didn’t work out too well. I can see it shifting the audio around but it doesn’t sound any “tighter” - just different - and I’m getting some strange echo/phasing side effects.

What is controlling how AAQ affects the timing? Is there a better tool/technique to use for this type of timing adjustment?