Though I think TigerTiger's post is quite near to be accurate, I have to say it is not all that certain as he points out. In my experience it is all up to how you negotiate and what is offered to you.
I had College students more motivated than language school ones and Language schools trying to get away with mega-low wages as well as skimming money wherever they could. The same goes for material and such things. It really depends on the school.
In general TigerTiger is right about the pay range of those institutions but everything else is really up to the school itself, the management etc. and in the end up to you what you ask for and what your base requirements are.
College and University are usually less well paid while private schools are more welcoming to higher pay demands. But what they offer and what you can get from them is really up to your negotiation skills and what you can offer to them.
College & Uni. is more the range from 4000-8000Yuan for fulltime also that is depending on what you teach (Economics courses are extremely well paid).
Plus that you can (or not) get allowances for things housing, return flights, work Visa (Z), etc but that doesn't mean they always offer it. Some only offer Z-Visa sponsorship (means they do the paper work but you still have to pay for it yourself).
Private schools from Grade K-12 are usually starting from 8k up to 20000 even 35000 Yuan but that depends on qualification and position. As well if it's an international school, quality standards, testing system, image ets.... I think for a starter in the Business with your background and depending on how good you are at your job if you get a FT-job over 10000 Yuan/month you got a pretty nice deal and if the company sucks, save a bit money and wait for better offers.
Besides some have Foreign Staff Management and some don't but that is really not depending on the type of learning center.
Also be aware that some Colleges/ Universities or other schools are not what they seem to be at least, not on paper. Its sometimes good to know when walking into the interview and HR person tells you how much this state-owned joint is suffering and then you hear reports that the School made multi-millions of profit the previous year.
I recommend get your CV's out get interviews, before you go to one research the school, about the things you need to know and if you are a good teacher walk in there, be confident, knowing what you want, don't settle for less you are worth, get the job....and show them how good you are on a day to day base....that opens a lot of doors to a great career. As it did for me and a lot of other great teachers.
My advise negotiate well, learn as much as you can about the backdoors, gray areas and tricks in the business. Be prepared but not scared and you will have a great time teaching in KMG.