Personally I would go with the Fuji because of the geometry. At 64 you aren't as limber as you were 35 years ago and the Fuji has a more relaxed geometry. For example I look at head tube lengths and the Fuji in a 54 cm frame has a 1 cm longer head tube than the Trek. This puts you in a more upright position. This bike was designed for the long time you would be in a saddle if you were riding in a Gran Fondo.
Component wise they are essentially the same. The other thing I would look at is maximum tire size that can fit in the frames. The Fuji comes with 28 mm and the Trek 25 mm but if you want to go bigger lets say to ride gravel roads could you fit a larger tire? I am a fan of disk brakes if you ride in the rain other than that caliper brakes work just fine.
If you are super fit and want a fast go to bike, then the Trek might be a better option. Also if you decide that you don't like the Trek it would be easier to sell than the Fuji.