After almost seven years of using MX Anywhere (the first model), I decided to upgrade after endless problems with the infamous double-click. So I will focus on the comparison between these mice. At first glance, the mouse has hardly changed since the unit. For example. The MX Anywhere 3 has defacto the same dimensions as the 1, suitable for control with the wrist resting on the pad. But something has changed for the better and something for the worse: 1) The mouse has lost weight. Significantly. I don't understand the manufacturers' obsession with making mice as light as possible. What is it good for? The old MX 1 had the advantage that the two AA batteries added about 46grams to the weight of the mouse, making it a pleasant weight of over 130g. That way you had the feeling that you were actually holding something, not just some cheap plastic box that you could move without much feedback (inertia).
2) The mouse uses the same size USB receiver as the unit, but has lost the chamber for storing it when traveling.
3) Instead of easily and quickly replaceable AA batteries, you'll now have to find a USB-C cable and charge your mouse every X days. This is both a plus and a minus.
4) Logitech does claim that the mouse supports Linux but that's kind of a lie. Although the mouse works under Linux, Logitech does not provide mouse setup software for Linux. And I guarantee you will need at least an initial setup, because of the wheel setup. Unofficial tools like Solaar, etc. do not yet support this model. You have no choice but to boot Windows and set up your mouse there. Fortunately, the mouse keeps the settings within itself. Also kernel 5.8, unlike the drive, can't recognize the battery, so you have no information in the OS about the state of charge. Maybe this will change in the future.
5) The wheel differs from the unit about the most. For one thing, it has lost the ability to tilt sideways. It is possible to emulate this by pressing the side buttons (and it works in the browser too), but it is not so convenient. Second, it can finally be used as a middle button, or in SW replace its function with a small bottom button that would default to switching wheel modes. But the tactile response of the click wheel is very very small, so I haven't decided which configuration I will use. For the third wheel you can adjust the resistance strength in step mode (the default has terribly weak resistance). It's fully metal, so it has nice inertia. Plus, thanks to the solenoids, you can switch on the "smartshift" function, which automatically detects fast wheelspin and temporarily switches to idle. That way, most of the time you don't have to manually switch wheel modes.
6) The main buttons are noisier than on the unit and that's saying something.
7) The price has risen to almost double that of the first model for no apparent reason.
To sum it up, compared to the unit, we have a worse mouse in almost all aspects for more money, where the only advance is the wheel. Even so, with the poor offerings of the competition, it represents a pretty good buy.