The funny thing with recumbents is that if you really want answers to your questions your are gone for years of buying - trying - selling - buying and so on.
No, I am kidding. Well, half kidding.
I have a limited experience but here it is:
- climbing: I never managed to climb effectively with a recumbent. Some people say that you just need to develop the right muscles which are not the same as for straight bikes. They may be right. Just that for me it never really happened. Maybe I should have tried harder.
- stability: I have an old long wheelbase bike which is extraordinarily stable at high speed. Stable to the point that you tend to lose all notion of speed, which could become dangerous given the poor brakes the beast has. I had a Bacchetta Giro 26 that was, as you say, more twitchy at high speed and needed to be handled with care. It was also clearly worse on bumpy roads - which improved significantly when I installed low-pressure Compass tyres.
I had bought the Bacchetta essentially because I was targeting long rides (randonneur events) and I was lured into it by all those people saying that you could ride forever without anything hurting. The reality is I would get tired much faster than on my upright randonneuse. So I finally sold it. In spite of this, I may well fall for another try with a lighter and more rigid carbon recumbent one day, who knows.