Show Gregor is a good deal smaller, slower, and less skilled than the book version, largely because of the impossibility of finding an actor almost 8 feet tall, let alone an athletic one.
I think that Jamie would win. The Viper managed to beat the Mountain and I would say that Jamie is a better fighter than him. Jamie does not have that many feats to boast of. We know that he is considered one of the best swordsmen in Westeros.
We also know that he is basically equal to Brienne of Tarth. Brienne has fought and beaten the Hound who in turn has fought the Mountain.
It could go either way, the Mountain is a brilliant warrior, but can I see him beating a prime Jamie Lannister? No.
Oberyn beat the mountain because he was the perfect counter to him. He was fast and flexible so the mountain couldn't catch and crush him and his spear kept him out of the mountains grip. Besides honestly Oberyn is probably a better fighter than Jaime.
Jaime being a swordsman won't fair well. He will have to go toe to toe with the mountains powerful blows and won't be able to get to the chinks in his armour without being in his range which is suicide.