I love debating Minish Cap (as it's my favorite handheld game) and I haven't had a long winded response to anything on this site in a LONG time. I used to be very active and still try to be but I've been busy and also haven't seen a lot of newer threads that required my knowledge. Anyway, here is my opinion.
I believe MC goes before OoT. My reasons are as follows. ALSO AS A NOTE THIS DOES NOT TAKE INTO ACCOUNT SKYWARD SWORD. I don't think any assumptions should be made with SS in mind til the game comes out.
1. The Backstory: We all surely remember the BS of MC talking about the Hero of Men and the evil that took over the land and the Minish people brining the HoM a sword and golden light. In the pictures of the BS the hero is in no way portrayed to look much like any previous Link. Any of the games that talks about a past hero who saved the world is 99.99% of the time talking about a Link of a previous game, but this one depicts a hatless (I'll get to that later) and long, blonde haired warrior. The only resemblance to Link is the green tunic (but again, there is no hat). I believe that this is a hero that has never been seen or heard of before and I believe it is a hero not of the Link lineage, thus putting it before any game with Link as the hero. It doesn't make sense to me that all these games would have Link as a hero and then in the middle of the timeline there was a non-Link who saved the day.
2. The Hat: Everyone hates this argument but it works SO well. I'll make it as short as possible. The hero in the BS (HoM) Doesn't wear a hat. Every Link ever has worn a hat at some point in their adventure, but the HoM is never depicted with a hat thus leading me to believe the HoM is not a previous Link and was around before any Link was around. In MC, Link doesn't have a hat, he has Ezlo. Had Link never met Ezlo, he probably never would have had a hat, thus it's obvious the hat tradition doesn't start til AFTER MC meaning any game with Link wearing a hat would take place after MC. At the end of the game Link is given a hat because Ezlo thought it suited him well. This is a possible sign that the hat tradition starts there. If you would like to argue that OoT starts the tradition because the Kokiri wear hats and tunics then listen to this. I beleive the Piccori become the Kokir somehow. I don't want to go too much detail into that because it would take forever but if you would like to hear more on my theory then PM me. Anyway, if the Picorri became the Kokiri then the tunic and hat tradition makes sense because the majority of the Piccori wera green tunics with some colored, pointy hat. The whole basis of the game is about a magic cap and stopping it's user. My whole point is that many hate the hat argument but the whole game is centered around the concept and importance of hats so saying the hat means nothing is stupid.
3. If this game took place anywhere but before OoT then Ganon/dorf would be a well known threat or well known, past threat, but he's not mentioned anywhere or even hinted at to exist. There are only three games in the series that don't mention Ganon/dorf at all. MC, FS and ST. FS has a direct sequel (FSA) that does feature Ganon/dorf so it doesn't matter that he's not mentioned in FS. ST is a direct sequel to WW/PH and in WW Ganon/dorf was the antagonist so it doesn't matter that he's not mentioned in ST. MC is not at all directly connected to any game with Ganon/dorf (based on my placement I put FS/FSA hundreds of years after MC) and if MC took place after OoT then Ganon/dorf would still be a threat but no one knows of him and no one mentions him. Some will say it doesn't matter because the game isn't about Ganon/dorf but another thing to note is that MC is the ONLY game that is Hyrule based and doesn't have Ganon/dorf in it (ST is new Hyrule after Ganon/dorf has been defeated so I don't count it). Strange that the greatest threat to Hyrule makes no easter egg mention/appearance whatsoever in a Hyrule based game.
I feel like there was more. I'll think about it and wait for some feedback before I go any further. PM me if there are any specific questions about any of my theories.