I would echo some of what Bobby said in his post... primarily that the big difference in 61 vs 141 is the number of hours it takes to get your commercial license - 190 vs 250. If becoming a commercial pilot and possibly a CFI is potentially in your plans, going 141 (for the entire training) will save you money and let you get there faster, so you can start earning money sooner. If professional flying is not in your plans, the cheaper method for just the private and instrument is usally pt 61. The biggest difference in the actual training requirements is that at a 141 school, you will be forced to have regular progress checks at certain stages of training to gauge your progress, and you will not advance to the next phase of flight until you have sufficiently learned the phase you are working on. Going pt 61, you are not required to have these stage checks, so your progress is less easy to track. 141 schools are required to use an approved syllabus, pt 61 is not. However, any professional private CFI or school using pt 61 SHOULD still use a good syllabus.
However, I am of a different opinion on the quality of 61 vs 141 training. I did all my training 141 at a flight school. I found that there were big differences in the quality of instruction among the various instructors at the school, just like there would be between various pt 61 private/independent instructors. I also found that I recieved excellent quality instruction from some pt 61, independent instructors. Ultimately I found that the quality and depth of the instruction I recieved was based on the professionalism of the instructor, not the sylabus or part(61/141) that the training was conducted under. The PTS, for which all training is based on, doesn't care either way, the same material needs to be covered. You can skim by learning the bare minimum to pass the check ride by going 61 or 141 just the same, and conversely a good instructor can provide excellent, in depth training under either format also. It really depends on the quality of the individual providing the instruction as to the quality of your training.
But as Bobby says, the primary decision should be based on your future goals. If you have no intention of becoming a commercial pilot and then a CFI, your decision should be based mainly on who you think will give you the most complete, in depth training. A pt 61 instructor can do very well, probably for less money in the short term, but he/she should use the same syllabus and cover the same material as the pt 141 schools do.
One other note. Pt 141 training is not very interchangable. If you decide you want to leave the pt 141 school, much of your training will have to be repeated to maintain your 141 status. Pt 61 training is almost universally transferable between schools and CFI's. If you complete 35 hours with a 141 school, then switch to another 141 school, you will not get credit for all those hours. If you went 61, you would get credit for them. However, some 141 schools have self examining authority (sounds kinky, eh

) which means they give your your final check ride and issue your actual license on their own. The benefit of this is that your are more likely to pass, and if you don't pass on the first try, it doesn't reflect poorly on your permanent flying record the way a pink slip from a designated examiner might, were you to fail a check ride after going pt 61. Ask your 141 school if they have self examining authority. It's a nice perk.
Good luck.
/Dave