Academy is more like an advanced training sim for Wing Commander II. I find it's good when you have a hankerin' to play with the ships from WC2 without having to play through the whole campaign. Also fun to challenge yourself with - set yourself up with six or seven Jratheks at a Nav Point, in a minefield, with you flying solo in an Epee, that sort of thing. And the gauntlet mode is nothing to sneeze at.
Whether or not you'd enjoy Armada depends on whether or not you enjoy strategy games. There's a lot of micromanagement involved with Armada, especially if you want a descent chance of winning it. I find the AI in the Armada/Campaign modes to be a little lacking on everything but the highest setting (and then a bit too much on that highest setting). That said, the gauntlet mode is worth trying at least once. And as far as the multiplayer mode is concerned, Proving Grounds works in the modern era. You can even set the game up to play split-screen; had many a fun Sunday evenings with my friends in my youth dogfighting one another on the same box. Armada/Campaign mode has to be done with one guy out of the room, of course, but it's still easily playable this way.
TL/DR: Both games are definitely worth it. Six bucks a pop at GOG.com (and they've been on sale fairly regularly over the last couple of years).