How do site optimizing & performance testing tools work ..

eg
I tried - websiteoptimization
and Firebug addon on firefox. BOth are cool but give different reports .

Also Google's tips code[.]google[.]com/speed/articles/ are different from Yahoo's -developer[.]yahoo[.]com/performance/


Which one should we try to make our website's comply with .. ? Is it a very difficult question ?

(sorry admins, i need to provide URLs. this is not for self promotion at all)