In the US there seems to be a progressive route that is prescribed I think mainly by medicaid and insurance companies. They like to give you a fixed pressure CPAP, and if that does not work, then an APAP, and if that does not work then a BiPAP. For the most problematic cases of central apnea an ASV machine is prescribed. My thoughts are that the only machine that has real significant treatment benefits for central apnea is the ASV. The others are pretty much the same, although certain types of BiPAP machines may behave a bit more like an ASV.
The basic treatment for central apnea is to avoid pressure. For someone that has both obstructive apnea and central apnea that is a problem, because of course obstructive apnea is corrected by pressure and centrals are aggravated by pressure. So where many end up is with a compromise pressure that is high enough to reduce obstructive, but low enough to minimize the centrals. I have a ResMed APAP machine, but I have found that I can control that compromise pressure best by setting it to fixed CPAP mode. For that reason I don't think an APAP is an obvious advantage. However it covers all bases as you can use it in either mode, and starting out in auto mode can help you find the compromise pressure sooner.
Essentially all the BiPAP does is increase the differential between inhale and exhale pressure. The CPAP and APAP are limited to 3 cm differential, but BiPAPs can go up to 10 or more. The problem is that this differential is a double edged sword. It makes the overall pressure higher, and can aggravate centrals, but at the same time it can simulate a breathing assistance effect which can reduce centrals. Certain machines can detect lack of effort to breathe and will trigger a backup cycle rate to assist breathing.
The ASV monitors every breath, and helps assist breathing on a breath by breath basis. It is the most sophisticated of them all, and often is the most effective with problematic central apnea.
This all said, you may not have central apnea at all. The normal way to measure it is in a lab sleep test. A trial APAP machine that detects central and obstructive apnea is often used as a confirmation method.