I'm still not very used to using this card optimally, but I think this card will see some play in Vintage. More than in Legacy or Modern. It's really awesome in control-combo type decks where you need that little extra draw to get your combo started, or that one card to counter a spell before you go off the next turn. Casting Gush, Misdirection, and Fow (Daze even, in tight situations) for their alternate costs, Mindbreak trap, and so on, with just two blue mana in mid-late game makes your deck much more threatening than Snapcaster. If you leave two or three blue mana up, the opponent has to think, 'are they going to cast Mana Drain? Mission Briefing? FoW and then Mana Drain? Misdirection then Mission Briefing?' etc. etc.. This is in addition to all the things that Snapcaster would normally be able to flashback, provided you have enough mana (which is usually not a big problem).
Two blue mana are not a big deal for blue decks (which are the decks that would be running this card main deck) mid-late game; if you draw it early you can pitch it to FoW or Misdirection, or put it back into the library with Brainstorm. Obviously for Pardoxical Outcome, Delver and such, Mission Briefing does not replace Snapcaster, but for many other decks, Mission Briefing seems to introduce many more interesting and effective aspects of play than Snapcaster.
I don't know how much play this card will see in Legacy and Modern. I don't think there are nearly as many uses with this card in either format compared to Vintage, given that draw spells are cheap, and counterspells are more varied and versatile in Vintage. That's what I hope, at least, so I can pick this card up for cheaper than it is right now.