Tough question, I have different answers depending on whether we are doing the comparison in terms of: 1) the games initial reception from gamers at the time of release, 2) my personal favourites based on my most recent playthroughs and 3) appeal to the general gaming audience in 2022.
1) Super Mario 64 > Ocarina of Time > Metroid Prime.
Mario 64 was an earth shattering experience in 1996. I mean just imagine going from playing Super Mario World to seeing a full 3D environment for the first time with chirping birds and trees that you can climb, etc. Mario 64 didn't invent 3D gaming but it took 3D gaming to a whole different level and really was the first game to nail 3D adventure gaming. Also, it is important to note that Mario 64 was also graphically insane when it released. It was one of the best made games in terms of gameplay quality but was also probably the best looking game in terms of graphics ever made in 1996. Even a super high-end PC in 1996 would struggle to produce the graphics that the N64 could handle. So just imagine that Nintendo charm and wow factor that you get when you play a game like Mario Odyssey mixed with the feeling crisp graphical realism that you got when you played Gran Tourismo for the first time on the PS4 and that probably wouldn't even be as good as how gamers felt when they first put Mario 64 into their N64s in 1996.
Ocarina was also a very impressive game at release and really moved the bar in terms of gaming (especially with regards to massive cohesive words) but Mario 64 had already moved the bar so much already that the wow factor that Mario 64 created was just more pronounced. Also, I feel that Ocarina was held back a bit more technically than Mario 64 was just because of the cartridges and the 240p resolution are not conducive to RPG's and large game play environments, respectively. Also, don't forget that by 1998, the N64 was a waning console where the PS1 had significantly overtaken it in sales. Sales of the N64 really died off after Ocarina's holiday season and so if you could consider Mario 64 the beginning of the N64's wave of success, Ocarina would be around the end of that wave.
Metroid Prime was an incredible game, but honestly it was heavily overshadowed by Halo and the XBox in 2002. Metroid Prime was a brilliant game that was released at the wrong time. It's sales were not great and lots of people complained about the lack of a multiplayer like Halo had (which is why Metroid Prime 2 caved and implemented a multiplayer, which I was disappointed with). XBox had better graphics and so even though Metroid Prime was a stunning game graphically, it just didn't move the bar much considering that Halo with all of its bloom effects and reflection mapping came out a year earlier. That said, Metroid Prime was a great game partly because it had the guts to not be Nintendo's answer to Halo. It had a beautiful, subtle and very intricate story and it wasn't focused on explosions, multiplayer and killing massive hoards of enemies. It was an adventure game that had elements of a shooter but that focused on puzzle-solving and uncovering the lore of the planet you are on. You could walk into a huge room with weird tracks on the wall only to figure out later that the wall was actually a giant morph ball puzzle that you wouldn't be able to solve until way later into the game, there are not many games (if any) that puzzle designs that were as creative and innovative as that in Metroid Prime.
2) Ocarina of Time > Super Mario 64 = Metroid Prime.
In terms of my personal view, all three of these games are easily in my top 10 (possibly even in my top 5). I love each of them in a very special, unique and timeless way and I will go back to play them again and again. That said, there is something absolutely brilliant and timeless about Ocarina of Time and its grand adventure and story that just makes it possibly my all time favorite game. I think that is really comes down the fact that I enjoy role playing games just a bit more than the platforming or shooter genres. Ocarina was more focused on puzzle solving and diving deep into the games story than on technical gameplay coordination, and that appeals to me just a bit more. So if I had to pick a fav out of these three it would be Ocarina. There are levels in Mario 64 like Tick Tock Clock that are just technically very difficult and there were bosses in Metroid Prime that I found really tough and it made me frustrated at times, I never had even a hint of frustration when I was playing Ocarina. The game is pure bliss.
3) Metroid Prime > Mario 64 = Ocarina of Time
There is no doubt that most gamers today (excluding myself) do no consider the N64 to be a console that has aged gracefully. Most do not like the look and feel of the 240p resolution and the N64 traditional controller is not well-regarded by most. The gamecube, on the other hand, has aged quite well. The graphics are way better than the N64, 480p still looks fairly decent on HD screens and the Gamecube controller has aged like fine wine. Frankly, in 2022 the Gamecube kills even the PS2 and Xbox in terms of appeal to most gamers. Also, Metroid has such artistic appeal in its graphics that I find that its graphical design has aged a lot better than the original Halo that focused on advanced effects for the time but that had fairly bland and redundant level design (especially after the first few levels). Every room in Metroid is meticuously modelled to be unique and that really shines through despite its age. I just think that if I was to give a new gamer one of these three games in 2022 who has no sense of nostalgia or memory of the past gaming era's, Metroid Prime would be the most accessible out of the three.
