I`m planning to purchase a Bach 42, and I just want to know what`s the difference between the 42A (with the Hagman valve), and the 42K, (with the balanced action "K" valve)? Which one is "better"?

The one you like better is the better one.

I play a horn with the Hagmann valve and it is definitely the best valve I have ever played. The Bach K valve is a similar design built by Bach. The Hagmann valve is built in Switzerland by a company that specializes in the valve. The K valve is built by Bach and thus I would expect it to have the same quality as Bach is known for. In other words, next to none. I reccomend the Hagmann valve. Of course, I generally reccomend a trombone other than Bach, but if you are set on getting one, you should test play a whole bunch any way you can get them, and then pick the best. Don`t worry about the valve, as long as it plays how you want it to. In other words, don`t set yourself up for a single type of valve and miss a good instrument that isn`t equipped with that valve.