How Girls und Panzer is a genuine sports anime while Saki is not
I've always felt that there was something different between Girl und Panzer and Saki, which it's reasonably frequently compared to. Recently I realized how the two are different in a way that makes the former a genuine sports anime while the latter is not. I know, that sounds inflammatory; given that Saki involves people playing a sport, how is it not a sports anime and if it's not, what is it?
My answer is that Saki is actually a shonen fighting anime in the guise of a sports anime, where the 'fights' happen at the gaming table and (generally) do not involve the characters punching each other. What makes the difference between Saki and Girls und Panzer is the presence (in one) and the absence (in the other) of magic powers and crazy special moves.
In Girls und Panzer the wins and losses depend on the actual strategy, tactics, and skills involved in the sport in question (in the real world). This is not obvious in GaruPan because there is no actual sport of tankery, but it's there none the less; the battles in GaruPan turn on actual things that real tanks and real tank commanders can do. This is not what happens in Saki. Saki is not really about mahjong and actual mahjong strategy and tactics (and usually low level play) are almost always irrelevant, in much the same way that punches and kicks are irrelevant background noise in shonen fighting anime. What the games are about in Saki and what determines victory and loss is who has what magic mahjong hack (and can use it best), in the same way as Naruto's victories generally turn on a carefully timed Rasengan or the like.
This is a large part of why Girls und Panzer is much more interesting to me than things like Saki. The presence of magic mahjong powers robs Saki's narrative of a great deal of predictability and suspense because the story becomes a game of 'okay, so what magic power is going to appear this time?' Conversely, the absence of unpredictable special tricks gives the battles in Girls und Panzer genuine tension and interest, because we can actually understand, follow, and predict what's going on (and in the process understand the problems Miho faces and make our own guesses at solutions). The reality of the contests makes them meaningful to watch.
(This is not the only reason that the battles in Girls und Panzer are good, because even with this the director has to make sure that you can understand, follow, and anticipate the action instead of getting lost in a muddle. GaruPan is very good at this.)
Girls und Panzer is not the only genuine sports anime, of course; there are plenty of them (just as there are plenty of magic shonen fight sports anime to go with Saki). For example, Cross Game is a genuine sports anime since the baseball in it revolves around real tactics and plays (instead of, say, some magic super-pitch).
(It looks like I don't watch much sports anime so I can't name any other examples off the top of my head with confidence, although from what I've read about it Chihayafuru is probably another genuine sports anime.)
Update: it figures that immediately after publishing this I remembered the other 'genuine sports anime' example I had in mind: Initial D, at least through the first few seasons. The car racing is probably not strictly realistic but it's real enough to feel grounded and limited, so you can understand the challenges that the racers face.