I don't think they're great literature, but I'm enjoying them. The writing is not sluggish. They're very much Space Navy books, with a fair amount of world-building specifically designed to allow for Age of Sail-type naval battles In Space, and not a lot of other technological development for a setting that's thousands of years into the future. The fight scenes are clearly carefully plotted out, with lots of important numbers slung about and plenty of casualties.
The main character is arguably a bit of a Mary-Sue, or if not that, it's at least clear that the author thinks his protagonist is super-awesome. And there are a lot of scenes where important social interactions happen on a kind of narrative level, where viewpoint characters just know things about what other characters are thinking and feeling.
In short, they're the sort of book that I would expect to get stuck partway through and never come back to. But as I said, I've read two already and am starting a third. So I guess David Weber is doing something right.
It's also worth nothing that he puts some serious work into maintaining gender parity, and that's pretty cool.