Both have their pros and cons - Personally, I keep both on my MicroSD card.
I picked Echoes of Time because I like the WiFI play - the Gladiators quests are great fun. People complain about the lag, but you get used to it if you play the WiFi much. If you find the lag that much of a problem, host the game yourself. The person hosting gets less lag.
Echoes of Time's cutscenes were horible. I prefer the non-prerendered cutscenes.
Ring of Fates is fun too, but once you beat the game it isnt near as much fun - few games are fun the second time around. If it had WiFi play I would like it too.
Even if you find Echoes of Time "too easy" there are nice cheats that let you switch the game to "Hard" "Very Hard" "Very Hard 2" "Very Hard 10" etc. On Very Hard 10, the weakest enemies do a lot of damage.
/me hopes they make another FFCC game for the DS or 3DS when it comes out - the FCCC series is one of the few I actualy enjoy. There are too few Action-RPGs in the style of FFCC for the DS. I like Hack'n'Slash Action-RPGs rendered in full 3D, real time battle system (preferably without a switch to a seperate screen)
It would be AWESOME if when the 3DS comes out they made a port of the FFCC game for the GameCube to it!
...wow this is a long post lol