I just switched from an FT-736R to an IC 9700 last March, somewhat reluctantly since I've had such a good run with the 736 since 1993. I only use the 9700 for satellite work, which is the same use I had for the 736 (I've never used a 910 so I can't compare that radio to a 9700). Thus, I'll confine my comments to the satellite arena.
My joke about the 9700 is that it is a computer that has some radio characteristics. In short, once it's mated to the computer and software, it truly is an amazing piece of work on satellite. It is a dream to operate at that point handling doppler compensation without any problem whatsoever. In addition to its ability to handle a sophisticated connection to a computer without breaking a sweat, it has some nice features for basic satellite operation. One of those is the bandscope which lets me find other stations on the linear birds almost instantly. Another feature is the "automatic frequency control" (AFC) which I use on the FM birds only since, once enabled, it will cause the receive frequency to lock onto the signal and shift with it as doppler changes (I generally don't find it necessary to shift the uplink frequency when using FM). It truly makes a world of difference for me.
I don't do EME (though I have thought about it and will likely try it in the future), so I don't have direct experience. However, there are multiple 9700 users that complain about frequency instability when using digital applications with it. Many of those folks have used a Leo Bodnar Reference Injection Board, which literally takes over from the 9700's internal frequency reference. It does require an external GPS reference clock. Here's a link to these accessories:
On a side note, you have probably long forgotten, but over 27 years ago, you were kind enough to take a phone call from me and answer some satellite questions when I really didn't know where to turn to find the answers. I really appreciated that and just wanted you to know that your advice was helpful and valuable.
Hope to work you sometime.
73 de Bernie, KF0QS