I would think it depends on whether you do your own servicing or not. If you pay someone else to look after your car, then a newer, less leggy car could well be very attractive.
If, on the other hand, you look after the car yourself then the advantage of familiarity and a deeper relationship with the car would count for more, I would think.
I am not particularly averse to the idea of buying another Morgan, but I find that every one I look at is quickly dismissed. Aeros and Roadsters have insufficient ground clearance to get up my drive, old +8s are too thirsty and unreliable, +4s and 4/4s lack power, and far too many of the cars for sale have daft light-coloured leather or inappropriate metallic paint. So each time I weigh up the disadvantages of my car - it's undeniably scruffy - and figure that it's not that big a deal after all.