There have been many "quiet" and quite touching moments in all of the series so far, not just about their own experiences, but also memories of family etc. Bob talking very openly about his dad's death and Paul spreading ashes in one of the episodes (not actually filmed) being two examples.
Bob is one of my all-time comedy heroes, so admittedly I'm biased, but a few notes on comments made so far:
Bob really does enjoy fishing, always has done (although didn't get out very much before Paul started taking him out more) and does go on his own outside of the making of the show (he occasionally refers to trips out and visits to tackle shops on the Athletico Mince and Parsnips podcasts, and a sketch in The Smell Of Reeves & Mortimer featured Bob fishing with his own equipment [replete with haphazard cast, from memory]), BUT he's always quick to acknowledge that the main reason he goes is for the peace and quiet, the scenery and time to reflect - he's never been one for the technical intricacies or perfecting the skills and isn't the least bit bothered if he doesn't catch;
The show is not about fishing in the same way that Jaws is not about a shark (and, if we're absolutely honest, even A Passion For Angling isn't really about fishing either, is it). It (Gone Fishing) is about two men who have both come out the other side of nearly dying (as Bob has said in the show a few times, he was actually technically dead for a good few minutes), being all too aware of and getting to grips with their own mortality and finding ways to appreciate the lives they have - it's very much therapy for them both, physically, mentally and emotionally;
Despite what some people think, Bob and Paul are genuinely very close friends and don't just put on a show for the camera. They've known each other for years - before both became famous in the early 90s - and spend quite a lot of time together. They have different personalities (shown by Paul getting annoyed with Bob's can't-really-be-arsed attitude, and Bob's amusement at Paul taking it so seriously) which is one of the things that make it a very real friendship and not just a face they put on just for the camera.
I think a lot of people go in with preconceived and/or misinformed ideas about both what the show is and what Bob and Paul are doing with it.