Just a follow-up on this: I decided to give Moneydance a serious try and migrate all my transactions over from Quicken. Exporting a QIF from Quicken and importing it to Moneydance was easy enough. However, due to the limitations of the QIF format there is no way for Moneydance to detect transfers between accounts with 100% accuracy, so there were quite a few duplicate transactions where it hadn't "guessed" right. Fortunately I could eliminate many of them in bulk using the Find&Replace extension. I also have a foreign-currency checking account which created some headaches because the exchange rates in transfers weren't always correct. All in all it cost me a few hours of my weekend to get all the balances correct.
It cost me another hour or so to set up automatic online import via Direct Connect, mostly because you have to do it for every account individually (12 accounts in my case), even if you have multiple accounts at a single bank. But once set up, it works well and seems actually faster than Quicken. Confirming transactions after importing is a bit different from Quicken (particularly for transfers between accounts), but works well once you get used to it. One limitation to be aware of is that Moneydance has no equivalent to Quicken's "Express Web Connect"; it only supports "Web Connect" and "Direct Connect". No issue for me though because I didn't use it anyway (mainly because I didn't like giving Intuit access to my online accounts).
I haven't really dug into the budgeting function (don't use it) and reporting options yet, but at first glance I didn't notice any glaring omissions. I use personal finance software mostly to track expenses and net worth, as well as to keep track of my investment accounts, calculate the cost basis for securities etc. It works well for these things.
I also tried transferring my data files from the Mac to a Windows computer and can confirm that the two versions are fully compatible. One license is good for several computers in a household, including Mac OS, Windows and Linux machines. There is also a mobile app that you can sync via Dropbox (with end-to-end encryption), but I haven't tried that.
If you are considering it, I'd recommend to use it in trial mode for a while and see if it works for you (the trial version is fully functional, but only allows up to 100 manually entered transactions). It does things a little different from Quicken and takes some getting used to.
Personally I purchased a license yesterday and will now run it in parallel with Quicken for a few weeks. If I encounter no serious issues, I will finally ditch Quicken and its stupid "sunset" policy and forced online activation for good.