f/2.0 on point & shoot vs f/3.5-5.6 on full frame

I was hoping someone can help clarify something. This is assuming all else being equal (at least as much as possible for this question.) If you have a p&s camera that has an aperature of f/2.0 vs a full frame camera that has an aperature of f/3.5-5.6, would thefull frame still be a better camera in terms of aperature rating?

Maybe I don't understand it quite completely so if I wrong in my thought process, please help me understand.

The reason why I'm asking is because even though the p&s has an aperature size of 2.0, it's still only hitting a small sensor size so even if the full frame had even a smaller apreature size, I would still think that it would still be better overall because f/5.6 on a full frame is stll better than f/2.0 on a p&s.

Am I right in this thought process? Please clarify if I'm not.