Frozen Synapse isn't the only turn-based Beta I've been playing recently. Battle Dex is also in Beta, and basically a cross between Advance Wars (though I find myself thinking of Battle Isle/History Line a lot) and a collectible card game. The cards act as power-ups, with you being able to take a handful with you into a mission. You can download it from here and there's a video and some more thoughts about how it all works below...
The cards seem to be functionally special-moves which supplement your hex-based maneuvering. Each one can only be used once - though you can take as many duplicates as you possess on a mission. The choice of which areas of your play you want to supplement depends a lot on your style, and a lot on the actual place the fight's occurring. So if a map's wide and open, you may want to go for cards which let you move troops around easily, for example. There's also special units and heroes which can only be summoned by playing a card. The actual resource that powers all this is gained from the mines, and can be spent on either playing cards or actually just summoning standard units. It really is Advance Wars meets a collectible card game.
At the moment you gain cards by competing in (and winning) tournaments and XP and similar, but with the "Buy" button you have to presume they're eventually going to make an option to spend cash on getting packs. They're also following the collectible game model in another way - there's tournaments with real-world prize-money. The first one was last weekend for $500, which isn't bad when you haven't spent any money on getting cards. I haven't actually played online, but there's quite a lot of single-player content, and you're able to play around with the full range of cards against the AI. It's really quite solid stuff - my only initial dislike is that the combat effects take a little long to play out for my liking. It's certainly worth a try. Get it from here.