It depends what you are looking for in your overall college experience.
I am guessing that, at Skidmore, you are considering the Health and Human Physiological Sciences major, since that is the closest thing to an athletic training major?
Skidmore is a more intellectually oriented, more liberal arts type of college than Quinnipiac. Your experience at Skidmore would be less about preparation for a particular career and more about science and ideas/ knowledge.
If you like ideas and want to explore a wide range of subjects, in addition to your major, then Skidmore is an excellent liberal arts college.
Quinnipiac will allow you to explore a wide range of subjects as well, of course, but it is more pre-professional. It actually has an Athletic Training major! It will give you direct training for that career. It has professionally oriented schools designed to put you into a particular career.
Skidmore’s mission is different. Skidmore will help you to explore ideas, and become a strong thinker and writer, skills you can apply to ANY career.
The student bodies are also very different. For example, for the Class of 2022, the median SAT at Skidmore was 1330 and the median SAT at Quinnipiac was 1180. Skidmore accepts under 30% of applicants. Quinnipiac accepts over 70% of applicants.
I am sure the admissions offices at either college can help answer your questions and maybe put you in touch with professors and students in your prospective majors.
Good luck and best wishes in your college search!