Yes, Contribution Based JSA (CBJSA) is not great. I worked for 30 years, paying over £100,000 in NI payments, and was told I could get £60 a week CBJSA for 26 weeks which works out at just over £1500- a tiny fraction of what I'd paid in NI.
But I suppose we should be grateful that there is something that isn't means tested.
I agree that the Direct Gov site is not clear. It just says your JSA may be affected by any occupational/private pension you receive, but doesn't say whether this applies to Income-based JSA, contribution-based JSA, or both.
The info on the link from Hounslow confirms what the Job centre Plus staff told me. Pensions above a certain amount affect entitlement to both types of JSA. So don't draw your pension until you've exhausted your entitlement to CBJSA.
Another gripe about CBJSA- it gives no entitlement to free prescriptions or free dental treatment. When I was on JSA I had to pay for my regular prescription medicines but I noticed every other customer at the pharmacy seemed to get theirs free.