Radio 3 has some brilliant stuff, but it's usually on at some inaccessible part of the day. It also has an awful didactic streak to it- you MUST listen to this, it's good for you. Usually expressed by putting on some dreary squeaky door stuff at 6.15, just as the alarm clock goes off and I want to stay awake. Switching to Radio 4 doesn't help- that's the time for the misery slot (i.e. economics news).
It's also noticeable that when they are armtwisted into putting on other stuff, they are as clueless and repetitive as Classic FM.

Joe, you have my full sympathy, a classical music lover and a cheese lover- in the USA. I bet you like good tea and real chocolate as well.