Robin vs. Raphael. Were it any OTHER Robin, I would back my man Raph any day. Raphael is not so much as a superhero but a warrior and unlike the more namby pamby Robins such as Dick Grayson, Tim Drake, or Steph Brown; he has and is far more willing to kill. And he has the physical skills to do so as well.
Jason Todd has the killer mojo working for him, but he seems to rely more on technology like guns and explosives to do his dirty work and I feel that Raph would be able to overcome him when it got down to hand-to-hand combat.
On the other hand, Damian is far more violent and brutal than Grayson, Drake, or Brown and trumps Todd in skill and cunning. But can he overcome a Teenage Mutant Ninja Turtle? Particularly the Master of the Sais and Sarcasm? I think that he has a better than decent chance.
I do think that this is a great match-up with similar skills and ruthlessness in both characters! For myself, I have always felt that in many of these match-ups; people seem to underestimate that some characters are always a bit more vicious, a bit more willing to go the extra mile which compensates for say a lack of raw power or skill as unlike their opponent, the more ruthless individual would be more willing to go for a more lethal or aggressive blow.
Were another TMNT facing Damien like Michelangelo or Donatello; I feel that they would underestimate him too much and would be annihilated before they could recover. Leonardo is iffy, but I think his sense of honor would be his downfall as Damian would take advantage of it.
Physically, I think Raphael dominates. He's stronger and has the reach advantage. Speed, I'm not sure which would be superior but I'm betting they're close. Finally, durability is something up in the air. The Turtles seem to be at least bulletproof on their shells and Damian is doubtless wearing some sort of kevlar and body armor; but as far as impact or knife proof? I think Damian's armor probably falls short there.
Next comes to skills. Again, they come close. Both were trained from childhood in combat. I think were it come down it; Raphael would exceed Damian in certain aspects in ninjitsu where Damian would be better and more broadly trained in a wider variety of skills like parachuting, deep sea diving, etc.; Damian would also be trained in a wider variety of hand-to-hand combat skills than Raph. Damian is trained on how to negate his disadvantages of size and proportionate strength and has gone up against metahumans to boot. I think that in this case; Raphael's physical superiority and experience would ultimately prove triumphant where it come down to a case of pure skill.
However, I think that Raphael has a number of disadvantages that Damian does not. First off, Raphael's weapons of choice; the sai are rather range limited unless he throws them. Then he's unarmed, so it's a last-ditch sort of tactic.
Damian has a utility belt and is armed with a number of throwing projectiles and weapons so he has a distance advantage. Next off, due to the fact that Raph tends to stay mostly underground in the sewers and stuff; I'm assuming that he is not as well equipped or knowledgeable about the environment above ground. Damian strikes me as the sort who is quite willing to hotwire a car and run his opponent down if he could do so; likewise he might turn a car into a firebomb.
Finally and most damning of all is Raphael's temper. He is the sort to lose his cool in the middle of battle particularly if egged on by Damian who will exploit this to the fullest. Against perhaps the most cunning and most vicious Robin of them all along with his skills? I'm afraid that Raphael is Turtle Soup.
WINNER: DAMIAN WAYNE!