My personal bias—especially for qualified teachers such as yourself—is to seek employment at a first-tier public university. There are several reasons for this. First, when you break down the ratio of salary and benefits to required work hours per year on an hourly basis, the university comes out way ahead (about 30% higher on the average). So although the gross monthly salary is higher at a private school, you are actually earning more per hour at any public university. I have an example of a typical salary breakdown under item #9 of our Comprehensive Summary Checklist for Foreign English Teachers in China
Second, because your workload and total work hours per year will be considerably fewer at a university, you will have more time to moonlight during the semester, and especially during the extended spring and summer breaks, if you care to. (In fact, most private English schools strictly enforce contractual prohibitions against outside employment while most universities do not.) In the end, you’ll wind up working fewer hours and making more money per year by working “full time” for a university and working part-time for a private school or even another university. The only problem with this arrangement is that it takes some time to familiarize yourself with the landscape and to get known among prospective outside employers.
Finally, if you can find a position at a high-ranked university (top 100 even is okay), both the overall caliber of the students and especially their English language skills are going to be considerably better than anything you will find at a private school. In short, the work is more enjoyable and vocationally satisfying at a university—unless, of course, you just happen to love working with kids and have the patience of Job. You can check the rank of any Chinese university by simply conducting an Internet search on “Chinese universities” and “rank” (although, now that I am thinking about it, I will probably add this list soon to the site).
Now, having just written all of this, it is of course possible to find a private school that actually values its foreign teachers more than, say, the foreign affairs officer at a particular university. So although I am providing you with accurate generalizations, they are just that: broad generalizations that don’t apply in every case. So you need to make a point of communicating with the university’s current (and preferably one or two former) teachers to specifically inquire about the sociopolitical atmosphere there for foreign teachers (as well as the other points I make in the checklist that is linked to above). But, generally speaking, yes, conditions at a public university for foreign English teachers in China tend to be better or, at the very least, far more standardized than they are at private English language schools (where variability in conditions and regard for the welfare of foreign English teachers is much wider overall).
If you have any other questions, you can feel to ask.
Best of luck to you!