The big difference between Part 61 and Part 141 is that Part 141 programs must be conducted IAW the standards contained in Part 141. These go beyond simply telling what it is you have to know and do for the certificate/rating, but also get into everything from the syllabi and documentation of training to the facilities themselves (classrooms, briefing areas, etc) to the airplanes (which must each be inspected by the FAA). In return for adhering to these standards, the FAA often reduces the aeronautical experience requirements for the certificate/rating, and other governmental agencies will provide funding for your training.
That said, there are plenty of local flight schools which have Part 141 certification, and "big formal" flight schools which offer training under Part 61 (usually in addition to their regular 141 programs, but at least in theory, possibly exclusively). Thus, Part 141 certification is not in and of itself a guarantee of quality training, and the fact that a school operates only under Part 61 does not mean the training won't be as good or better than a "big formal" 141 program. Only a good "pre-purchase inspection" and due diligence of the schools you're considering will give you a good idea of how good any school is.