I don't see the difference between "Come on" and Allez/Vamos, all of them can be directed to self or opponent by the meaning. I mean, it depends on how loud and openly you do this - Hewitt is known for that. But for example, Gael does pump himself up with Allez rather loudly, too, that can be taken as a taunt by the other player I think.
Fair enough, I don't have nearly enough of a mastery with these other languages to read all of the nuance in the various connotations. I am always happy to hear as much elaboration as possible.
"Let's go" in English, which is the closer equivalent to "Vamos" and "Allez" in Spanish and French, sounds more innocent than "Come on," which is often more pointedly directed at another person. It's similar to "bring it on," in a way.
I'd like to see them start yelling, "U MAD BRO?!"