The HH books are way more ... masturbatory.
About military hardware, for one thing; I can picture Weber being someone with bookshelves full of volumes about military stuff, and really being into it.
About politics. Weber's a right-wing military republican and so are a lot of his readers, and there's a huge amount of smug self-satisfaction in it at times.
The heroine isn't an author avatar but rather she's the author's paragon; she's a bit too perfect, and her flaws are, while definitely there and definitely obstacles at times, the kind of flaws an author's pet tends to get, because they're "acceptable" flaws. She also doesn't get to learn or change all that much.
If you're like me, that means that there are bits that I have to hold my nose through in those books.
The blessing is that all the dubious stuff is just window-dressing to the main point, which is the war. The politics and the character's personal life doesn't intrude on the good bits, and the good bits are most of the novels. Weber's a flawed writer but he's good at military strategy, tactics and action, and let's face it — that's why one reads his books. For me, it makes them guilty pleasures, because I know that there's a lot of crap to them, but enjoyable nonetheless.
Bujold's books, while superficially aimed at the same kind of audience, are a whole bunch deeper and more satisfying. For one thing, Bujold is not writing her fantasy of an ideal society. I suspect her ideal is actually a lot closer to Beta Colony than Barrayar, but the messier, bloodier reality of Barrayar is simply much more fun to write about. Her characters aren't paragons of goodness. Barrayar has done some truly horrible things within living memory, although the core characters are all trying to do good things (Aral, Cordelia, Miles, Ivan, Gregor etc.).
A brighter future for a darker age.