Hate to nitpick, but Burnout wasn't part of the Need for Speed franchise
Maybe you're referring to the fact that the developers eventually took over development of the franchise from EA Canada.
For me, the peak of the Test Drive series was Test Drive Unlimited. It was a brilliant game, which while not perfect, did introduce a lot of innovative things and took the series back to its roots. It introduced an open world and had an online component that it sort of used as copy protection, ie if you didn't have an online connection, you wouldn't have access to everything and wouldn't be able to complete the game 100%, and used the online component as a sort of hub to populate the game world as people would cruise around, explore and find races. It seamlessly integrated itself into the game in a way that many games only wish they could do. As an example, I was once cruising around minding my own business when I met someone on a road and we ended up cruising together. It was popular enough that EA went on to make Need for Speed World, although I don't know if that has an open world to the same extent. Test Drive Unlimited 2 came out and had a lot of problems.