Hahah, I got that Timewalkgames email and did the same thing!! I googled "Crimson Echoes vs Flames of Eternity"
I have played through Crimson Echoes, and can honestly say it is a great game! (I am a big Chrono Trigger fan so that probably helps!)
I have always been curious about FoE, (and I believe there is some bad blood between the two development teams)
The story I read made it sound like when the CE team got the Cease and Desist from Square, the FoE team grabbed the unfinished CE ROM, and basically made minor changes to it so that they could call it "theres", then finished it and called it FoE,
Problem is, then the CE ROM got "leaked", and if you play both side by side you will notice how similar they are...
If you are only going to play one of them, I would choose Crimson Echoes...
However, if you are a crazy Chrono fan like me, you might want to own these as well:
Chrono Trigger - Original
Radical Dreamers - graphic Novel SFC satellite sequel to CT
Chrono Trigger - Prerelease Promo Cart
Chrono Trigger - Crimson Echoes
Chrono Trigger - Flames of Eternity
Chrono Trigger - Famicom / Chinese NES pirate cart
Chrono Cross - incredibly underrated / beautiful game!!