Both my dc have been through Horsforth High School.
It has good and bad points but overall, and compared to other secondary's in the area, I liked it.
I think its strengths are its academic side - lots of success in national competitions for science and math's for instance.
Weaker point would be the pastoral care ime. When one of my dc had a broken leg the school were not particularly helpful with the logistics of being in school with a broken leg. I've heard other people with similar tales.
That being said, it doesn't have an issue with bullying as far as i know. The pupils are generally well behaved (I work around the corner) when I see them out and about. They don't wear blazers but are pretty strict on the rest of the uniform code etc. and pupile tend to look smart.
I think my dc were both seen as 'middle of the road' in academic terms and perhaps at times I felt that some of their teachers didn't even know them at all.
It only takes pupils now from the LS18 postcode so if you like the school take that into account!
Can't tell you much about Pudsey schools except I have a few friends with DC at West Leeds in the performing arts stream and they love it!
There is quite a lot of choice in Leeds for schools compared to other areas I think. If you lived in Horsforth you could always look at Ralph Thoresby or Abbey Grange (C of E) too. Even the 'bad' school in the area - Lawnswood has changed in recent years and lots of people actively choose it for its amazing facilities (big school so well funded) especially for dc who might be considering a more vocational route into careers etc.
Good luck with the move, I love living round these parts 