I have trained under both part 141 and part 61. I obtained my private license part 141 through a flight school in Virginia. It was an absolute nightmare. The program was so bogged down with red tape that it took much longer than it was supposed to. There are absolutely needless restrictions with part 141 that really restrict both the instructor and the student. It sounds like a good concept, but like with most things the government gets its hands on, it is a bureaucratic web.
Part 61 still has many requirements that need to be met, but it allows the CFI to customize to the students needs. Any good part 61 program will also include some heavy ground school.
Keep in mind that at the end of the day, both programs end with the exact same FAA checkride.