I do not know those machines personally, but can comment on after 6+ years going from a small single boiler (Silvia) to a large HX machine (Vibiemme Domobar Super). The Silvia had been PID controlled for the last three years or so.
A PID does little to nothing during the shot. It replaces the thermostat and so supplies the user with the ability to set and hold a specific temperature while idling which potentially gives better shot-to-shot repeatability by removing that one variable. Once the button is pressed to brew the PID has virtually nothing to do with making espresso.
On the other side of the coin is the HX design. Although it would seem that the pressurestats that HX machines use for temperature control would seem to be less effective, but brew temperature stability comes from the design of the HX itself. take a look at the
Domobar Super review here on HB on page 6 there is a chart showing 5 pulls (thanks to Dave for those, BTW):
... Check out how consistent the results were. It is quite impressive. Not saying that this specific machine is necessarily superior to all others, but that HX design can supply some very consistent results as well as allowing simultaneous steaming and brewing.
Using the same coffee, and with all the experience I had with the Silvia, the stock Domobar made better espresso right out of the box. There are a lot of reasons for that (heavy E-61 brewhead, flow rate control, etc.), but there it is.
So I would say that just because a machine has a PID does not necessarily make it superior to a machine not PID equipped. In the case of the Silvia, the PID is used to overcome the poor response of a button thermostat which has such a wide deadband that it detracts from the benefits of what is otherwise an excellent design for a small single boiler machine.
Finally- how long will you keep the machine? Ten years? A machine that is $500 more than you plan on spending costs about $4 a month over what you are planning to spend over its life. If, like me, you are the kind of person that keeps things around a long time then spend it now and enjoy it over a long time period.