Previous 7 plus owner here. Received the Max today, like others I find the phone more comfortable to handle than the 7 plus, much more so. I wouldn't recommend it to people with small hands (or people who prefer small phones period), but this feels a lot more ergonomic.
It probably helps that the phone feels faster and the screen is more responsive. Part of comfort with the phone is not just carrying it around, but how much effort is required to do routine things, no matter how minor. The gestures on the Max just seem to glide, and Face ID (something I was skeptical about) has been super speedy in all types of light.
As everyone has noted, the screen is lovely, and though I have yet to really stress test the camera, it's a good upgrade over the 7 plus. My 7 plus was a bit cooler in terms of color temperature, so the warmth of the Max screen is a small adjustment. I prefer to watch lengthy videos on a big screen like my OLED TV or the iPad Pro, but I'll definitely enjoy watching shorter YouTube videos and even half hour Netflix/Hulu shows on the Max, not only because of the screen but because the speakers have more dimensionality and are louder. It's a really nice experience.
One thing that was really painful on the 7plus was running the Apple Podcast app (yes, I tried to switch to Overcast, but for a number of reasons stuck with the Apple app, poor as it was), especially simultaneously with a mapping app and CarPlay. If I didn't give the podcast app time to load before driving, it would just stutter or crash, and CarPlay would sometimes not connect with the 7 plus. (often, it was just faster to connect via Bluetooth). Even when a podcast played properly, the screen wouldn't show the play/pause controls but just a queue of podcasts -- playback had to be controlled via the phone.
(All the above assumed that CarPlay wouldn't automatically play the first song in your Apple Music library at ear-splitting volume, instead of the podcast you wanted...yup, that "feature", which would also kick in at random times)
Tonight, I connected the Max to my VW unit via CarPlay while running a quick errand, and BOOM -- automatic connection, podcast played immediately. Started up Maps, zero problems coexisting with other apps running while driving. Navigating the podcast via CarPlay, super smooth. Can't wait for Waze to be available via CarPlay soon.
Everything else has been a pleasure so far with the Max -- apps launch faster, reading on iBooks/Kindle and dedicated apps like the New Yorker have been great. I agree with people who say smartphones have matured to the point that going from the 7plus to an Xs Max is an iterative upgrade functionality-wise, compared to say, going from the 4 to the 6 or 7. But it's a strong iterative upgrade, and early on, I'm happy.