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Private - Really doesn't matter...most 141 schools would seem more reputable since the FAA has to approve their aircraft, instructors, maintenance and syllabus. It could possibly seem more organized. The King/Cessna schools work really good, as do the Sporty's and Jeppesen I would imagine. Benefit of a King/Cessna school is the ground school comes on CD (for Instrument and Commercial as well)
Instrument - You'd be crazy not to do it part 141 if you can
Commercial - 60 hour bonus here. Part 141 allows you to follow a syllabus from Private through instrument to Commercial allowing you to complete your training with similar flight requirements but lesser total time. For example, the King/Cessna system at minimum times would complete a student regulaly between 190-200 hours. However, due to higher dual given requirements of a 141 course, associated cost may be EQUAL or just slightly less. 190 hours compared to 250 is a pretty good deal...and then you can get your CFI...and the less hours you have to pay for the better.
Advantage...141
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Like ESF and Doug said there are some great 61 schools out there that blow the socks off of 141 schools (of course there are also some 141 schools that blow the socks off of some 61 schools). I think that if you prefer a 61 or 141 school depends a lot on personolized preferences as well.
I am planning on doing my ratings all at a 61 school. For me it is the perfect fit. I know the owners, the instructors, and the mechanic very well, and it offers a nice variety of equipment. They follow the Jepp syllabus BUT it is a lot more flexiable. The way I am approaching my training is similar to the way one would at a 141 school. During the summer I was there 4 or 5 days a week flying or getting ground done. Once our season is over I plan on being there 7 days a week to get my ratings done.
I have been flying a lot lately working on my instrument rating and the I have come to the conclusion that ther is NO WAY I would want to do that rating at a 141 school. In my opinion I want to be absolutely solid on my instruments and the concepts behind them. To have a syllabus layed out at a 141 school that I had to follow would not be for me. The instrument rating is one that I am working on now and I am having a ball doing it. I have been flying all through the NY B Airspace in actual conditions getting some great experiences that I would not get if I were at a 141 school.
For me the 61 school is a perfect fit. I started my PPL training in April of this year and I plan on having my CFII done by next May or early June. I will be close if not at the 250 hour mark and I will have a good concept of the ratings I hold. It will also be a little cheaper than if I were to go through a 141 school.