As is so often the case, the best answer lies between these two options. One of the weaknesses of a high percentage of collections with no fixed fee is that the medical billing company doing the old AR clean-up has no incentive to pursue smaller claims. It will cost well over $20 for each old claim worked by the medical billing company. This means that any claim under $100 will not provide much profit for the company and will likely be ignored. This is an issue because many of the older AR claims are these smaller claims.
The fixed fee option, however, has its own problems. The problem with a pure fixed fee pricing model is that the medical billing company has no real incentive to collect as much money as it can. The company is being paid a flat fee; if it can write off a claim it will cost the company less but, of course, cost the medical practice more in lost revnue. In addition, under a fixed fee model, the medical billing company has an incentive to take a long time to work the old AR - the longer they work, the more they make.
A hybrid model of a moderate fixed fee and a moderate percentage of collections provides the best of both worlds. The fixed fee component makes it economical for the medical billing company to pursue smaller claims. The percentage of collection means the medical billing company will profit from collecting every dollar that it can (and thus does not have an incentive to just write-off claims).
Proper alignment of incentives between the practice and the medical billing company cleaning up your Old AR is critical. A mixed pricing model provides the alignment of incentives that is required for the best overall results for the practice.