They're a bit different sounding. The K712 is a little warmer and has more fullness and body, a little more bass, a blacker background, sounds a little more smooth and liquid-like, and is a little more open. The K702 Anniversary is a little lighter, drier, faster, airier, and more intimate.
Personally, I prefer the sound of the K712 overall, but I think the Anniversary looks better.
The main advantage I hear on the Anniversary is it having the air be a tad more forward in the mix. The K712 still has air, it's just less forward. I think the timbre of instruments sounds a little more natural on the K712 though. Also, the K712 is slightly less intimate sounding thanks to its deeper pads. Having more body while simultaneously being a slighlty more open is a cool combination and can work well for classical.
It's not definitely not as drastic as the difference between Q701 and the Anniversary. It's more like it trades the Anniversaries upper mids and dryness for more overall body and a more liquid sound. Luckily, the soundstage doesn't sound any smaller like on the Q701>Anniversary, because the K712s deeper pads cancel it out. I think one of the main reasons the Q701>Anniversary sounds more intimate is actually because of those closer pads, more-so than the actual warmer signature. I did a lot of pad swapping between the two and the pads made a bigger difference in how intimate the soundstage was than I thought they would.
While I appreciate the Anniversary's greater sense of air, there's also something a bit thin, harsh, and peaky somewhere in the mids that bothers me a little when I go back to them after listening to the K712. The K712 smooths out the upper mids even more and is just really rich, full, and unfatiguing sounding. It's one of the least fatiguing headphones I've heard.
At first when I tried the K712, a kind of missed the edgier upper mids with female vocals, but once I adjusted I didn't really mind - and when I went back to the Anniversaries I noticed that those upper mids brought with them some dry peaky harshness that bothered me a little.
So those edgier mids can be double-edged in that they can sound good for some things like enunciation with female vocals but have the potential to harshen some other things. The K712s rounds them off a tad but also adds better body and fullness to compensate and keep the mids interesting. It's an area where I could see some people preferring one way to the other, but I found myself preferring the K712's approach as it sounded more full, natural, and less fatiguing.
The objects/instruments sound larger and meatier with more body yet at the same time the K712 still manages to have a slightly larger soundstage then the Anniversary. The pads play a big role in that. This is one of the things that sealed the deal for me on the K712. It's always impressive when a headphone pulls off body alongside an open soundstage, and the K712 does this more impressively than the Anniversary.