Colleges attached to a university.
Same as universities except:

Students are usually those who failed GK. They are not motivated, and most don't want to work. You still need to pass them for exams, however a degree from one of these colleges is pretty worthless. Many SS eventually realize this and are further demotivated.
Sometimes the university college cares more about the money than teaching.
Often no foreign affairs office. If you need help you are often on your own.
Staff are sometimes valued sometimes not.
No flights, people are usually recruited locally.

Hourly rates of pay are common.

Universities.
Students have all passed GaoKao (GK) the college entrance test. They are usually more motivated, but cheating is endemic and you have to learn to live with it.
University Deans expect students to do well in exams. They don't want to know about cheating. If the exam is too hard it needs to be moderated. This goes against the grain, but it is their house and their rules (This is China). Occasionally you will get students who never attend class, and these you can fail. The institution really cares about the students.
Teachers are expected to be on time and sober. That is the biggest gripe that any institution has about teaching staff. Get this right and you can dance with the devil and they don't mind. The schedule is fixed at the beginning of each semester, and so life is organized. Teachers must take attendance, it alsocan protect you from students who fail. In addition to your teaching you may be asked to give 1-2 evening lectures per semester on a general subject about English, or US/EU culture. You may also be asked to run or attend English Corners, I usually suggest that these are better organized by students. You may be paid for evening lectures, you will not usually be paid for English corner. Teachers are expected to prepare and mark exams, andou do not get paid extra for this.
Contracts are usually for the academic year only. Paid spring break, no paid summer break. Contracts are usually for a maximum n (often 15) teaching hours (50m) per week. Any more and you get overtime. For public holidays, they jiggle the calendar, this is usual in all places of work here.
Medical cover means you can go to the campus clinic/nurse. You also have emergency only cover at hospital. This is not full cover.
Accommodation is provided free. Look for those that offer an apartment. They may be basic but they are self-contained and you have 1-2 bedrooms, living room, kitchen, bathroom.
Access to the canteen which provides cheap food at set times only.
Flights home are paid, but sometimes they only have rules that allow for direct flights (this works in your advantage) but will only pay for port of Exit to port of entry. A disadvantage if you need a connecting flight.
Visa provided. If they like you, and you like them, you can sign up for the following year before you leave with will give you a longer visa.
The University will have a foreign affairs office to manage foreign teachers affairs. This means you always have someone to help. At least one member of staff here speaks English.
Staff are valued highly.

Public Vs private sector advantages and disadvantages as I see them, I am sure others will chip in.
Firstly, there is a spectrum (not continuum) of providers in both sectors.
I will break this down into separate posts otherwise it will be too long.

Another thought.

Buy a vehicle in the city where you are based if you can. Or at least one where you will spend a lot of time. This will make servicing and repair much easier, especially if you are one of their own customers. Additionally, unless a special order, that dealership will carry more spares for the vehicle.

Perhaps you should avoid a grey import. Local dealers may not want to know if parts are not the same. Especially true for any bodywork. If they don't have a parts list for that model they may not want to know. It is hard enough to get people to take responsibility for their own job here, let alone something out of scope. Specific models can change a lot from month to month, and the model is identified by chassis number. However, Chinese dealers may not have access to chassis number data for grey imports. Any parts you buy, will be at your risk. You may also have warrantee problems.

If you want to spend a larger amount of money look at the Jeeps (made in Beijing) are cheaper, or the Landcruisers.
If you only need the larger load area occasionally, consider a trailer, I don't know the rules on these here, but I have seen cars with tow hooks.

@Mike
Well, not at a bar/cafe anyway.