The Stagecoach site isn't that bad. But the lack of a route list for each opco has always really annoyed me as it's something pretty much every other operator has. I actually much prefer the layout of the website they had from 2005 to 2010 as it was much more accessible, although dated in design now. Stagecoach are also very poor when it comes to maps. So quite often if i want to see services they have in a particular area i find it much easier/faster to use Bustimes. I will however give huge credit to Stagecoach in that it's very easy to work out fares from A to B and generally the journey planner (although i loathe them) is decent enough.
The First site isn't too bad, but it's quite dated and can be cluttered in places. It's also one of the less reliable frequently having downtime. Fares are also near impossible to work out. Much like Stagecoach the website they used from around 2006 to 2011 was much better.
The Go-Ahead websites are okay, they do the job but are by far the most cluttered.
As for Xplore/National Express (Bus division). Their site isn't too bad, there is a route list for each opco but it's not as easy to find as you have to search for a route before you can get the option to go to the route list page. They do typically have network maps but these again are the the simplest to find (You have to go to the route list page, useful information and then "network maps").
The McGills website is rancid, You have to download the timetable/maps to view them which while not the biggest burden ever is a huge annoyance. A shame because the general layout isn't bad, although the route list is rather tragic.
"Lothain Group" (LB, LCB, ECB, Green Arrow etc) actually a fairly decent website, although timetables are not as easy to find and you can't go from one website to another, you have to manually input the URL or google search. Route maps are okay, although they still use the rather dated and complex spider map design. The main page is also far too PR driven, rather than having useful information such as major service updates right in the centre they have them offset in a small box to the side. Instead the main page is covered in adverts for their merchandise, Coffee Shops etc.
Borders Buses. Probably one of my favourite sites, although can be slow at times and the home page isn't that attractive.
As for Arriva, i don't need to comment much more other than that ever aspect of it is rancid and dated. I'll never understand why Arriva decided to use the colour of my Grandparents old 1980s "Mint Green" Sofa. Every thing you hover over seems to create a pop up that covers the entire page.