It is the weakest link - goodbye.
Seriously whatever is your slowest component is going to slow you down in any situation.
You could be talking about two different PC's? Then the configuration of those will also count into which is faster on ethernet hard wired or wireless.
If it is the same PC then fine. Hardwired is going to be that little bit faster and might I say a little bit more secure than the wireless option. Whether it is fast enough to notice that's another question.
Is your internet access that slow that you need to speed it up?
If so you end up paying more for a better connection.
The other thing to consider is what sites are you connecting to? We are all at the mercy of the routers, servers, and connections of all the sites out there. So again it's back to the weakest link, smallest component etc.