I have no idea why anyone would want to 
Why not take the best parts from both machines to make the best you can then sell the other one?
Unless it is extremely rare and in storage or NIB and you are trying to make some money from it.  I can't see the point.
You only have one pair of arms and can only play one at a time 
As for a competition, other than NBA which would be cool to play head to head, why not play 2up on the same machine, more fun watching each other playing, and individual machines of the same title often play very differently so not a true competition anyway unless you use the same machine.