You listen to the first guy and ignore the second guy.
Well, why? Both of them equally invoke the authority of God, so God cancels out as a basis for decision. Why isn't it OK to listen to the other guy instead?
Let's take that out of the realm of religion and see how it holds up.
Barack Obama and Rudy Giuliani both say they will be excellent foreign policy presidents. They both say that they know how things work on the international stage, and have the strategies that will defeat the Islamists and other enemies. Obama wants to bug out of any place where we might kill someone in Al Qaida and also have tea with Chavez and Ahmadinejad; Rudy wants to kill terrorists right and left and be tough with Chavez and Ahmadinejad. Both equally invoke patriotism and say they will be great in the job, so doesn't that mean I should listen to them equally?
I know you can bring up another religion besides Islam and try to make the same argument, but I think it's worth noting that the guy who said "God wants you to love your neighbors as yourself" allowed a bunch of Roman PFCs to torture Him to death as part of those ideals, and the guy who said "God wants you to kill the infidels" committed petty genocides, assassinated a poet who made fun of him (while she was a nursing mother), used late-breaking bulletins from Allah to "win" arguments with his wives, and consumated a marriage with a nine year old as part of his ideals. To say that these two faiths bring similar evidence to the table is kind of silly.
Oh, and as for why I should listen to Jesus instead of Muhammad (or Buddha, etc.)...let me know when they come up with a guy who rose from the dead.