Edit: I'm not trying to be rude (it comes naturally). But you just explained "great" as "better, with more". I guess smooth might mean faster, which might be because it isn't doing ads and tracking. It seems to come back to third-party being the crucial difference, and "app" not mattering.
Third party clients could be webapps, too, of course.
I don't think the reddit clients work this way though.
I used Boost. Its ads were not intrusive (and I despise ads) and the UI was written with a small touchscreen in mind. If not for my distaste for phone keyboards, I'd say it was a better experience than the website on a desktop.
Would it be possible for a mobile browser to have a better experience? I don't know. I value my sanity too much to do web development. But Reddit was absolutely determined to make its mobile site unusable and the official Reddit app had a bad reputation (and I wouldn't give those bastards the satisfaction after being nagged so much to install it), so a 3rd party app was the only reasonable solution.
I'm on old.reddit.com too and I use the mobile app (including the 3rd party ones back when they existed) for one primary reason: Two windows I can quickly switch back and forth on. On my phone I use Reddit to look up things. I can have a Reddit thread on one window and a Google search on the other and go back and forth. In a browser switching tabs back and forth is painful, often reloading pages, losing the spot in the browser, having this url bar and top bar taking up tons of screen space.