Part 141 schools operate a fixed syllabus that the FAA has inspected and approved, which lowers the private pilot minimum from 40 hours to 35 and can lower ATP eligibility to 1,000 or 1,250 hours for graduates of an approved program. Part 61 schools work to the same regulations for certification but without the approved syllabus, which means the schedule bends around you rather than the other way round.
In practice almost nobody finishes a private certificate in 35 hours or 40, so the lower minimum is theoretical for most people. The real difference is structure: 141 suits full-time students who want a fixed program, 61 suits people fitting training around a job, and both produce the identical FAA certificate.
We are Part 61, and we say so plainly because there are two situations where it matters against us. If you intend to use VA education benefits, most flight training benefit programs are tied to Part 141 or degree-linked programs — see our page on GI Bill flight training for the honest version. And if you specifically want a restricted ATP at reduced hours, that requires an approved program with an FAA authorization.
Everywhere else, the part number is the least interesting thing about a flight school. The scheduling, the instructor and what is inside the package price are the whole answer.