IMO - Stamford is a large town. It has proper shops - like Marks & Spensers (sort of like Sears/Macys). Many tea houses, pubs & restaurants. As we don't have kiddos, I don't know about the schools, but I do seem to recall a prestigious school being in Stamford.
Oundle is wonderful. I've lived there for 7 years, and I still love it. It's a small market town, but has 3 coffee shops, post office, GP, 2 dentists, Coop (Food Store), etc. There's a primary, middle & secondary school in town. There's also a good private elementary & 'prep' school. I have lots of friends with kids, and they all seem to be happy in Oundle! There are two playgrounds, lots of baby groups, etc. There are a decent number of Americans, from the nearby base (I think Molesworth).
If you have any other questions re: Oundle, please give me a shout!