Crimson Echoes is the original version of the ROM hack. It was shut down during beta testing when the creators (who were developing here at the Chrono Compendium) received a Cease and Desist from Square Enix. This obviously upset a lot of fans who were eagerly looking forward to this hack, so one of the beta testers apparently "leaked" the unfinished beta into the wilds. The version that was leaked is 100% playable, it only lacks polish and some additional changes that were intended.
Some time later, Flames of Eternity was created by an (supposedly) unaffiliated third party, who took the leaked, unfinished beta and went about providing much of the needed cleanup, in addition to new spells, some new character sprite sheets, etc. They also added some additional content, such as an explorable 2300ad.
The two are largely the same. Flames of Eternity is surely the more complete version of the ROM hack, although it lacks some of the original creator's intent and has some minor changes to the story and dialogue.
Play Flames of Eternity if you want a less-buggy mess that isn't completely true to the original creator's vision; play Crimson Echoes if you want it as the original team intended (but were unable to completely polish).