Link has a better (if not better, different, but im saying better) grab game. A vertical kill throw is a stronger asset than a ledge kill throw, his grab is longer ranged by a very significant margin, and he gets better combo's at almost all percentages. I believe that dthrow uair is a kill confirm on certain characters, but I am not sure on the details. Its a pretty hard confirm to get down pat, but its pretty good in his metagame. Bair is an interesting combo move that can have setups using only a single hit ala melee falcon nair. Don't quote me on this, but I think 1 hit bair -> spin attack is a confirm he has. Uair is a pretty cool move, it can be an airdodge trap by itself (but Link's speed makes this less useful than it would be).
In general, he is pretty damn different from Tink. Fair is a 2 hit with crazy power, range, and low landing lag. He has Zair that is much longer... his bombs are more for zoning and trapping than confirms. His nair is a really good edgeguarding tool, and the huge difference in his regular and fastfalling speed gives him good mixups offstage. His Dair is also way better, I think? If you are pinned in shield it is a great pressure tool compared to a meh stall-n-fall, and it really hurts when it hits. Spotdodge hurts it, but if you time that wrong you take a hard hit.
Wind boomerang is a pretty cool tool as well. You can really do a number on someone, and it synergizes well with his ranged usmash. He also is heavier, which is something I particularly enjoy in my characters =P
I'm no link expert, and im sure I just scratched the surface, but they are very very different characters. Pretty much every move is significantly different in their use. If I was pressed to say a random, important reason why you would choose slow link, I would say that it would be his dashgrab. That is an amazing midrange dominance tool, and it really has some painful followups. Zair is bretty cool as well.
EDIT: Reading this, I know someone is going to say it: Yes, Link has confirms from his bombs much like Tink. But for reasons often discussed in this thread, they aren't as large a part of his gameplan. Tink is likely to come in throwing a bomb, being all floaty and trying to confirm it to a fair at the ledge for a kill. Link can do this, but it carries all kinds of different risks and isn't as much a staple of his play, from what I understand.