It could go either way.
Obviously, I don't have canon sources as this is a speculative answer, but here goes.
Diary Tom Riddle has certain advantages. He is young, and healthy. Depending on the fight with Harry, He may or may not have Harry's wand, quite similar to his own original wand.
Old weakened Voldemort has a different set of advantages over young Riddle. He has Experience. Voldemort was active as a powerful wizard for quite a while. He has steeped his mind in cunning for decades. I suspect that he has become even more ruthless since the creation of the other Horcruxes. He is also used to paying the Long Game. He makes plans that take years to come together.
So we have the classic Youth vs. Cunning matchup here.
Old Voldemort is going to try subtlety in an effort to move young Tom around for an alliance at first. He is going to know young Tom is to betray him in an effort to take all of the power, followers, and such for himself. Old Voldy will lay in preparations for this. Old Voldy will also be quite willing to kill Tom quickly if he feels he is getting to strong. Voldy will want the alliance for one reason: to take young Tom's body over. How exactly, I don't know. I am pretty sure older Voldemort will lie in wait until he's sure he has the method figured out and supplies and whatnot near to hand before he even reveals himself to young Tom. Then we will say Hi, maneuver Tom in to just the right position, and then strike like the serpent he is.
But don't discount young Tom either. Even though he is the 16 year old Voldemort, he is still Voldemort. He will expect treachery, especially since he will be trying to set something up himself. His moves won't be as smooth, but Tom is strong. Even if he gets out-maneuvered, it's possible he could simply power through the traps.
If young Tom survives, he will be at a disadvantage that increases over time. He won't just have Old Voldy after him, he's going to get the Ministry down his back. Dumbledore will take steps, and Fudge might not be so squeamish about going after a low rent Voldemort. His position won't be nearly as weakened by the admission that Voldemort came back through a Horcrux and it's a 16 year old Voldemort as well. Fudge may just say he's after Tom Riddle, not Voldemort at all.
Old Voldemort will still have most of his network of Death Eaters, though some will shift to young Tom. Voldemort knows where all the bodies are buried. Voldemort will have more shadows, since Fudge will still deny his existence.
So, up to confrontation and first betrayal, they might be evenly matched. After that, Young Tom is on borrowed time.