AP Physics C is the calculus based physics option and the one most often expected from engineering applicants.
Two separate exams
Mechanics is one exam. Electricity and Magnetism is another. They can be taken together or separately, and they are scored separately.
Mechanics is the more commonly taken of the two. Electricity and Magnetism is the heavier one, both in content and in the calculus it uses.
The calculus question
This is the deciding factor. Physics C uses derivatives and integrals as ordinary tools, not as an occasional flourish.
A student who has not yet reached integration will spend twice the effort on Electricity and Magnetism: learning the physics and the mathematics at the same time. Taking Calculus alongside, or the year before, changes the workload substantially.
Against Physics 1
Physics 1 covers similar mechanics topics without calculus. Physics C treats them faster and more deeply, and assumes the algebra is already comfortable.
A student who has taken Physics 1 will recognise the topics in Mechanics and still find the treatment new.
What universities read
Engineering programmes read Physics C as the stronger signal. Some award credit or placement, and the policy varies by institution and is published on the institution's own pages.
Which one to take
If the target is engineering or physics, Mechanics is the baseline and Electricity and Magnetism is the stronger addition. If the target is medicine or biology, Physics 1 and 2 fit the ground better.