I feel somewhat capable of providing some information on the subject, as a good friend of mine is an owner of a Duratec powered Caterham, and I spend a lot of time tracking my 997 with the Lotus group here in Houston, and have had a bit of seat time in many flavors of 7's and Elise's on the track.
Frankly, I'm baffled by the common comparison of the M3W and the Caterham. The only things the two cars share is the fact that they are small, British, and impractical. This hasn't stopped the press (Top Gear, Fifth Gear, etc.) from providing wonderfully enjoyable comparisons that make for great entertainment, but aren't particularly instructive.
The Caterham is a track day weapon, bred with it's first priority being handling. The car is responsive, dynamic, fast, and unforgiving. It appeals to those who value the driving experience first and foremost. They are iconic but ugly (sorry

), without any concessions to styling whatsoever. This is part of their appeal, I love them, and would love to own one someday, but they are a specialized tool for a specific task - driving quickly and precisely.
The Morgan 3 Wheeler isn't any of the things the Caterham is. It really doesn't handle all that well, it isn't particularly fast, and it's 3 wheel geometry is fundamentally flawed. The Morgan has no place on the track at all, BUT it has more character and style in it's left front wheel that an entire Porsche Panemera. The Morgan is for owners who want to be different. It's for folks who want to drive at moderate speeds around town, or through the countryside and have more fun doing so than most anyone else. The Morgan is for the owner who would also like to own an MGA or Austin Healey 100-4 (Sorry, I'm not a fan of the 3000's

)' but who doesn't want the headache of owning a 60 year old rust bucket). I think the Morgan appeals to folk who want a vintage experience in modern guise. On nice days, I'll take my Morgan to work (local drive, no highways) in a heartbeat over my 997 Turbo. It get to talk to car people about the car at every gas station and stoplight, and I draw a crowd whenever I park. No one ever wants to talk about my Porsche...
So there you go, my 2 cents...