There are good and bad of course, to both sides of this debate.
Private schools are generally less expensive, smaller classes, usually the same instructor, and usually run by a former massage therapist.
However, in a smaller school, you will likely have to bring your own clients in, your credit may not transfer into school hours, and you may have to pay for your own supplies like lotion, sheets, possibly a massage table.
Public schools are usually more expensive, larger classes, several different instructors (that may only teach a specific subject), and usually is run by someone in business.
However, you may have more study resources, possibly receive college credit, if there are more students then you can network and study with them, and you may be able to work out a payment plan for class.
The main point of finding a school is choosing one for the right reasons.
The biggest complaint I hear is that students don't correctly understand anatomy and massage technique, and since this is your focus, pick a school that will teach you everything you need to know! I highly recommend taking a course that is perhaps slightly longer than what you state requires, it will enable you to stand apart from your peers in a field that is very competitive.
Take your time and visit as many schools as possible, you will find the place that fits you best!
Good luck!