eMacs predate SATA. They use PATA drives:
A lot of 1,25G eMacs have bad logic boards--a lot!
See if the newer unit's serial number falls into these ranges:
- G8412xxxxxx- G8520xxxxxx
- YM412xxxxxx - YM520xxxxxx
- VM440xxxxxx - VM516xxxxxx
The program that fixed the issue expired several years ago.
The HD will fit and operate, and all of your apps will still work. However, the OS X system may not work. The gray install discs that come with each model Mac are usually unique to that model Mac. But those are relatively close, so it may work. Did you get the system install discs with the "new" eMac?