Assuming that both characters would be going at it at their maximum potential, I believe it would be a close fight but Link would win. Noooo, Ikeee (T.T)
It's given that both characters can at least withstand a hit, be it through HP or Hearts. Link is adept with many long range weapons that could either stun or knock back Ike. If Ike were to attack with Ragnell at a long range, it would hurt Link if it hit, but Link is nimble and capable of finding openings to dodge or counterattack. Ike is capable of dodging long range too of course but I don't think he would be able to keep up a long ranged battle with Link.
Now if they were to come into close quarters Ike could deal heavy damage to Link, especially if he activates Aether. But that wouldn't stop Link from counteracting with a Spin Attack or equipping his Magic Armor. Maybe that's too cheap >.> If they were to get into a deadlock I don't think Ike could overpower Link. Link has withstood deadlocks with Ganon and pushed back Gorons (with a little help). He has definitely demonstrated his strength.
It's actually really fun imagining this fight in my head.