The '02 4 cylinder 626 and the '00-'03 Protege/Protege5 both use the FS-DE 2.0l engine. The one used in the BJ Protege/ Protege5 makes a bit more horsepower N/A (5hp I believe) than the 626 did, and obviously more in Mazdaspeed trim.
I know the automatic transmissions in the 626 were horrible and failure prone, but I don't know enough about the manual used. I would imagine the manual in the later Protege/ Protege5 are stronger, especially since they were revised with stronger forks towards the end of production.
The 626 and Protege lines both use the McPherson struts with a twin-trapezoidal suspension geometry out back.
I think the Protege line has a small advantage in the engine and drive-train dept if comparing 4-cylinder to 4-cylinder (not enough to write home about) and it should stand out in the handling dept. since there are probably more parts available suspension-wise for the Protege line.
There are definitely a lot of similarities under the very different body work, but they are still in different classes as stated above (compact vs mid-size.)