Like I said, read up and familiarize yourself with mma and the ufc. This is all recent stuff you can find information even on this forum.
For basic starters, just to begin with-
Rashad and Lyoto were light heavy weight CHAMPIONS.
Their career primes and greatest achievements were at light heavy weight. They were both undefeated when obtaining CHAMPIONSHIPS at, guess what? Light heavy weight.
They didn't move to mw untill Jones destroyed them making it impossible to stay at lhw. Their careers were/are in their twillights.
The operative word regarding all these fighters including Shogun, they were CHAMPIONS. That means they were the elite echelon, further rashad and lyoto were undefeated.
Read up, fighter chronology is available on this site too