Remakes aren't quite as prevalent in gaming as they are in movies, and they take on a different form. Generally in movies a person wants to apply their own artistic view on a subject so they remake it. In games a remake tends to be a few minor gameplay tweaks and a major overhaul to the graphics. Case in point: the remakes of the early Final Fantasy games for the DS and the Monkey Island 1 and 2 remakes. I'm explaining this to create a clear line between a remake (re-creating and updating content), re-imagining (redefining the source material in a new and usually drastically different light), and reboot (forgoing source material and sustaining core elements). This article is only discussing merits for a remake, as that was the original question.
Story
Both these games have landmark stories, but they couldn't be more different. One involves time traveling to save a princess and a kingdom and the other… well, I've read dissertations on the story of Final Fantasy VII. Simply put, a lot of people love these stories all based on taste, it's simple vs grandiose. In my opinion Final Fantasy VII comes out ahead, the narrative in this game is epic, and deserves to be experienced by a new generation.
World and Setting
Hyrule is awesome, it harkens back to the day of good 'ol swords and sorcery fantasy, but we've seen it… a lot. It's been seen in different forms and while not hyper realistic HD graphics (wow!) it has been thoroughly done. It pains me to say this because I really do love Zelda games, but something needs to change. It's pretty sad when the Final Fantasy series is more innovative and adept at trying new things. Final Fantasy VII has a robust and engrossing world filled with characters to chat up, side quests to undertake, romance, action, adventure! It has it all! Ocarina and VII have beautiful worlds to explore, but just based on sheer variety I'd have to go with Final Fantasy VII.
Gameplay
This is another category based solely on opinion, because honestly is just comes down to which genre you prefer. Ocarina is a fantastic action adventure game while FFVII is a great JRPG. One has you swinging a sword and grappling to walls with the press of a button the other has you strategically planning your next five moves. However, Final Fantasy VII also showed us just how many amazing mini games you could squeeze onto three PS1 discs. Whether snowboarding, riding your motorcycle or piloting a submarine, this game had quite an abundance of extras that were worked into the story incredibly well (even the ability to replay them!).
Ocarina had some great dungeons and puzzles (including the infamous Water Temple). The combat would still be the same essentially, no matter how HD it is. I don't really care if I can count all the hairs on Clouds head as he swings his ridiculously phallic sword, or if I can see the thread count in Links sweet hat. I can't really choose a winner in this department because somedays I'll feel like an action game, somedays a JRPG. As for applying new technology though, I think improved AI would make for some fascinating and intense battles in Final Fantasy VII, can you imagine if the Weapons were smarter?
Other remakes/re-imaginings
Ocarina was a great success and Nintendo does this funny little thing whenever it has a great success: It remakes that game over and over until it stops being successful. Zelda and Mario are the worst offenders here. There is no denying that Ocarina is a great game, it is certainly one of the all time classics, but it has been remade again and again (referring to the similarities in Zelda games since Link to the Past). I don't really have an issue with playing the same game over and over with minor differences but when it comes to a remake, I'd rather a game get remade that hasn't been done so many times. Also, looking at how the Zelda games have evolved what would you get with a remake? HD graphics, maybe some voice acting NPCs, and perhaps some enhanced puzzles. Enemy AI could be improved but you'd still just be swinging a sword or shooting your bow. Link still won't talk… and he's no Gordon Freeman.
On the Final Fantasy side of things you have an interesting trend. Much like Nintendo a few years ago Square Enix realized the last game that people really loved was Final Fantasy VII, so they decided to go back and milk that cow till it was dead and dry. They made new games in the FFVII universe and told new stories. A sequel movie and game and two prequels. It was a great time to be a FFVII fan, for the most part. The games on whole lacked the charm of the first thus never struck a chord with the fans. Though Crisis Core remains one of the most well written and intricately woven prequels I've ever played (and it's fun too!).
Each respective franchise has seen it's growth and changes, but I think Final Fantasy has grown more and would have more to offer for a remake. Now, do I think FFVII will ever be remade? No, but that comes with a caveat. Square Enix holds the FFVII remake as a trump card, basically if they were ever to screw up so badly as to alienate their entire fan base *cough* Final Fantasy XIV *cough* they could throw down an announcement that they are remaking VII and everything would be right again. Now, here's why that will never happen. First, fanboys: they will always defend and love Squenix. Second, it would be nearly impossible.
Final Fantasy VII is such a huge, rich and deep game that to recreate the world and bring it to todays standards (Voiced NPCs, Cutscenes, fully rendered backgrounds) it would take Square Enix 30-40 YEARS to finish according to Final Fantasy XIII Director Motomu Toriyama. As for Ocarina of Time being remade, yes, I believe that will happen.
Ultimately though I don't think a remake of either of these games is necessary. They both had a huge impact on me and I don't need to experience them any other way than how the were intended. Yes, both would look stunning simply from an artistic standpoint, but honestly it's not that hard to pick up either game in it's original form and still be floored by it, and I think that speaks more highly of a game's merit than any remake ever could.