TDi = Turbo diesel injection
TDCi = Turbo diesel common-rail injection
LX = The trim of the car
Zetec = The trim of the car (this one has got more extras than the LX)
The TDCi is a newer engine and more powerful, responsive and also gives you better fuel economy.
I would certainly go for the second one all though if something goes wrong with the injectors or anything like that, it would be more expensive to repair but you would probably save in the long run.