To be fair, part of the reason for that is the thicker, scratch-resistant magnesium body that makes it more weather- and dust-resistant. The new, five-axis in-body stabilization also adds weight, and it's got a much larger grip, another nod to working photographers that wield large, heavy lenses. That does help with handling, as unlike the X-T2, you can haul the X-H1 around by the grip with little fear of dropping it.
The electronic viewfinder (EVF) on the X-H1 is the best you can get on any APS-C sensor camera. It's incredibly responsive, activating in a third of the time as the one on the X-T2 when you raise it to your eye. It's also bulkier than on other Fujifilm models, though.
Fujifilm has cloned the top dual-dials from the X-T2, and they're a pleasure to use on the X-H1 and feel incredibly solid. On the left, the upper dial controls ISO, and the lower one lets you change shooting settings (continuous, single, etc.). On the right, you can set shutter speed on the upper dial and autofocus settings (zone, single-point, tracking, etc.) on the lower one.
There's no longer a top dial for exposure compensation like on the X-T2. That has been replaced by an LCD display, like the one on Fujifilm's medium-format GFX-50S, so exposure compensation is now controlled via a button and dial combo. The LCD is handy to see key settings at a glance, but you can see that info on the rear display and I'd rather have the exposure compensation dial back, to be honest.
The X-H1 has a new, hair-trigger shutter that I still hadn't quite figured out when I gave the loaner back to Fujifilm. It was easy to set it off by accident, especially when half-pressing for focus, so I have a lot of pictures of the ground (protip: use the back focus button). I'm sure I'd get used to it with time. Otherwise, handling is by and large the same as other Fujifilm models, apart from a few oddities. The "Q" button to change common settings is located in a slightly different, more awkward-to-reach spot, for instance.
The larger body and odd handling might not please all Fujifilm fans. Although the in-body stabilization does add bulk to the camera, it really does work well, however. To best sample the new feature, I requested a test lens (the 35mm f/1.4) without any built-in stabilization.
For still photography, I was able to get sharp shots with shutter speeds as low as 1/8th to 1/15th of a second or so. Without a stabilized body, I wouldn't usually shoot below 1/30th, so this really helps out in low light situations. It worked just as well for video, smoothing out small movements like handshakes better than other models, including Sony's A7R III. Unfortunately, unlike most other cameras with built-in 5-axis in-body stabilization (IBS), you can't assign the setting to a button but have to scroll through menus to turn it on and off.
The electronic front curtain shutter -- which starts the photo electronically and ends it with the mechanical shutter (after the exposure is complete) -- is another cool new feature. There's no EVF blackout while shooting with it at up to 1/8000th of a second, and a built-in shock absorber prevents image-blurring vibrations. That makes it a lot quieter than the X-T2, but purists still get a light clicking sound. If you'd rather do things the traditional way, the X-H1 also has a mechanical shutter (1/8000th max), and a silent electronic shutter (1/32,000th).
The hybrid autofocus system, with both phase- and contrast-detection, is nearly identical to the one on the X-T2. However, Fujifilm did tweak its algorithms to increase the speed and improve low-light performance. There are five AF-C presets accessible by the lower-left dial, depending on whether you want to track faces and static subjects or action scenes. You can also fine-tune each of those settings depending on the situation.
For moving subjects, like our bull terrier dog who loves to randomly tear around the yard, I found that focus-tracking worked best when I kept him within the phase-detect pixel area. Outside of that, it tended to lose focus.
On most subjects, though, the AF system was rock solid: At the end of the day I had very few out-of-focus shots, even when I shot quickly. While the X-H1 has Fujifilm's best autofocus to date, it's not quite as good as the systems on comparably priced Sony and Nikon cameras. The TTL 256-zone metering is also excellent, but in low light, white balance tends to be on the blue side.
As for shooting speeds, the X-H1 can only handle short bursts of 31 RAW frames when shooting at its maximum 8 fps speed with the mechanical shutter. In electronic shutter mode, it can handle 14 fps for 27 RAW frames before the buffer fills (it has dual high-speed UHS-II card slots, so that helps). That's not too bad for its intended market, but Sony's A7R III, which has double the resolution, can handle 78 RAW frames at 10 fps.