Is it better to be specialize in car engines instead of being a general auto technician?

Probably more work for a general mechanic. People bring cars into shops for all sorts of problems, brakes, suspensions, radiators, electrics. So lots of call for people with general automotive knowledge. Engine work only would generally be in a specialised shop doing custom rebuilds and engine recons for general mechanics.

Also with modern cars, brush up on your computer and electronics knowledge. A modern car has more computers than the space shuttle did, and you are more likely to be dealing with wiring or sensors when you fault find an engine.

The transmission and engine are the most complicated parts of a vehicle. The other stuff doesn't require any training.