I used to install a lot of Pyronix Enforcers and still do for tenanted properties as they are happy without an Internet connection, in fact I am installing one this evening. Installation wise, the Ajax is a bit quicker as its just a case of scanning the QR code on the sensor, pushing the adopt button then configuring it in the app. Functionality wise, I think that the Ajax is more intuitive, smarter and easier to configure. Also be aware that Pyronix is likely to EOL the Enforcer in the next few years as they have totally maxed out the CPUs capabilities, so its unlikely that any more development will happen with the Enforcer range, hence the Pyronix AX Pro series which looks remarkably like the Ajax. Also in Europe Ajax is pronounced AyAxe which sounds very much like AX, you can draw your own conclusions.
Ajax are marketed and sold as an installer only product, hence them spending a lot of time on PD6662 and BS EN 50131 Compliance and are Grade 2 Certified
They have some really novel detectors that Pyronix dont offer, such as curtain beams, outdoor dual curtain, outdoor PIR with Cameras.
Overall I have more confidence in Ajax than I do Pyronix, as Ajax are more stable in the loss of internet connection (they dont need the manual reset that many of the Enforcers do) , they offer Lan, Wifi and upto 2 independent SIM cards for connection / failover and their products are always in development. Other than stability of internet connection, they are both great alarm systems but really serve different markets. Enforcer is much cheaper to install than an Ajax system. But the Enforcer is a 25 year old panel and its starting to show its age.