As others have said, a Caterham is a very different animal. But as with Caterhams Morgans are available in a number of different guises and you need to understand what you want to achieve and select the model accordingly.
As a very rough guide the Roadster and old +8 are more GT touring than sports cars, though as Morgan has shown the new 3.7 Roadster can be a potent track weapon.
The new GDI +4 is possibly the best all round model, especially if ordered with a narrow body and the 4/4 is a rev machine that I found tedious on a long run. It is a sports car, rather than a tourer.
After trying a 4/4, an older +4 and a 2009 Roadster we went with the Roadster and with modifications (Suplex front suspension plus brake reaction bars, Rutherford AVO rear Dampers and a few other details) it suites our needs perfectly. Our only real criticism is the gearbox: it is slow and a bit notchy: the Mazda box used in the smaller engined cars is far faster. Quite why MMC didn't use it in the S2 Roadster I don't know.