See, the difference between TMC and SS is the amount of detail put in.
I'll agree with that, but I'd like to point out that that's the
only difference. In terms of function and significance to the plot, they are the same.
The function of the relationship in
The Minish Cap is purely to get Link personally involved with what's going on, in that case stopping Vaati. Because Link cares for Zelda he wants to save her from being trapped in stone, so he embarks on the quest which quickly becomes about stopping Vaati instead. Likewise, the function of the relationship in
Skyward Sword is purely to get Link personally involved with what's going on, in that case stopping Demise. Because Link cares for Zelda he wants to save her from being trapped in crystal, so he embarks on the quest which quickly becomes about fulfilling Hylia's plan instead.
In terms of significance to the plot, neither relationship really matters after the quest begins. They are motivation, catalysts, and nothing else. This is why
The Minish Cap works even though Zelda spends almost the entire game trapped in stone, and why
Skyward Sword works even though Zelda spends almost the entire game in different regions or trapped in crystal. Yes,
Skyward Sword has a few moments were Link sees Zelda but these are only used to remind us of what we already know: Zelda and Link care for one another. The scene were Zelda seals herself in crystal includes a little bit of exposition to help the plot along but that is separate from their personal relationship. The moment might be emotional because they care about each other, but it doesn't change the plot or Link's motivations, and so isn't really all that important. It doesn't teach us anything new or move their relationship in a new direction (she still believes Hylia's plan is more important, he still just wants to get her home).
Skyward Sword presents it better and makes it easier to connect with, but at a fundamental level both games use the same relationship for the same purpose. The level of detail doesn't change what the relationship is, just determines how well it pulls it off.
I personally find that relationship to be a bit bland. It's just too generic for my taste. Link cares about Zelda so he runs off to save her when something bad happens. It's the most basic it can be. They can tart it up as much as they like with sailcloths and crying but it just doesn't interest me all that much. That's why my choice would be
Spirit Tracks or
The Wind Waker, if the latter had made better use of the premise.
In
Spirit Tracks, Zelda is a key part of the quest, actually helping Link directly to save the world and stop the bad guys. The fact that she's a ghost is a nice little quirk that adds a bit of flavour to it. She's an active participant, whereas
The Minish Cap and
Skyward Sword, and many other games like
Twilight Princess and
A Link to the Past, use her in a much more passive one.
The Wind Waker really could have made her an active participant, and she is a little bit while she's still Tetra, but once she is revealed as the princess she immediately goes back to being passive, which is one of the only things I would criticise that game for.