In Home Assistant, the primary way to do anything is to use Integrations that plug into your monolithic Home Assistant application.
In WebThings, there is a robust model for putting your devices online that other services & applications can script. It's also built around very nice sets of standards[1], which means you don't need to use the WebThings Gateway or the WebThings Thing UI. For example there's a web based 3D ui using AFrame[2]. to demo it's use, there is a fake/demo standalone webserver pretending to be a solar roof[3]. Not high production, but being able to hack out a WebThings standard ui or device at a lightning pace is extremely impressive.
A lot of folk are well served by the monolith, but long term, having everything bound up in a single technology stack, having to live with every choice Home Assistant has made, is extremely unappealing to me personally.
I've started moving my ZWave stuff over to WebThings. I'd like to add my LiFX equipment too. Previously I had just been using some Node.js scripts I'd authored myself to control these devices & to record energy consumption. It was a fun project, and I had been doing some kind of similar but not as good decoupling work like WebThings does, but I'm looking forward to having an API-first means of doing this work, and especially excited to see semantic web / jsonld baked in from the start.
[1] https://iot.mozilla.org/wot/