Okay, Rating these two on a few levels
Survivability: Kane has been around for well over 100 years, surviving numerous "deaths".
Eliphas has been around for around 10,000 years. He has "Died" only once, and gone to HELL ITSELF, but managed to come back a few years later
Winner: Draw
Resources: Eliphas has/has had around a company or two of Chaos Space Marines, numerous Cultists, and the occasional demon.
Kane has a F&*%-ton of cultists in a semi-regular army, Though they also have tech on level with battle titans and Skitarii.
Winner: Eliphas
Planning: Kane has had to instigate several World Wars to achieve his goals. In general, he has been in control of the situation for a good deal of time and demonstrates exceptional forward planning and manipulation
Eliphas...
. Lost the war on Kronus, and lost the war in Aurelia, but managed to turn a chapter of ruthless superhuman killers against their indoctrination to join the forces of chaos
. Impressive, but in-game and in cutscenes he never really seems to have a plan or be ENTIRELY in control of the situation.
Winner: Kane
Personal Combat Abilities: Kane is never at the front lines
Eliphas has fought on the front lines for over 10,000 years (give or take due to the fickle nature of the warp)
Winner: Eliphas
My Personal take on the situation: Eliphas invades earth and manages to get GDI out of the picture quite easily (for handwaved reasons). Assuming Kane knows better than to engage in an all-out war, or gets to mass-producing Avatars and Marked, I would predict a VERY long war as Kane struggles to take down the hard to replace Chaos Marines. If he manages to accomplish that (hijaking the ion cannon maybe?), Then Kane wins due to how bad chaos cultists are.
If Eliphas is able to attack NOD's major facilities early on? He wins through sheer quality.
SO, my overall pick would be... Kane actually. Assuming they fight on Kane's "home" turf, Eliphas won't have cultists to rely on. Kane would therefore have superior numbers on a tech level roughly similar to the Imperial Gaurd, but with more fanatical troopers. It would be a close run thing, but I would guess that Kane already has a plan in place to deal with hostile invaders from hell.
Of course... Neither would die permanently. The fanbase would resurrect Eliphas and Kane has villain immortality.