Does it feel old because it's something you played a long time ago, or does it feel old because you feel it has aged poorly? If the former, then that's your own opinion, but I really don't think it can be the latter. In order for something to age poorly, it needs to be outdated, which Re:CoM definitely isn't. Nothing has stepped up, taken CoM's battle system, and made it so much better that everyone went "Wow, I can't believe we used to use the card system in Re:CoM, it's terrible now compared to this modern version!", it's just too unique of a battle system.
To word my previous question differently, does this "old" feeling feel more like playing a traditional role playing game like Dragon Quest IX ("Wow, this turn-based gameplay feels so old, it hasn't changed since the 80s and I find it boring.")? Or does it feel "old" like Goldeneye on the N64 ("Wow, ever since the GCN/PS2/Xbox came around with their dual analog sticks and made console shooters so much better, this game is almost unplayable! The controls are outdated, they feel obsolete and I find it boring.")?