After you've looked at a couple you can usually ID them pretty quickly, look at Scubapro*with exception of Mk17 and a handful of others* or Atomic's lineup and compare it to say Apeks/Poseidon for a good comparison.
Pro's/Con's
Diaphragms used to have a significantly lower air flow which caused piston's to be preferred for a while, but Diaphragms are not flowing more air than the valve can provide, so this is a nonissue and anyone that brings it up is reading 30 year old data and assuming technology hasn't changed. Airflow is essentially irrelevant at this point, any modern production regulator can flow more air than you could ever use.
Pistons are a simpler design and used to be cheaper to make. Again, at this point technology has caught up and they are about the same price point for comparable designs. Apeks DST vs. Scubapro MK25 for example.
Diaphragms are easier to seal thus generally better suited for dirty/muddy water conditions i.e. sump diving, and ice diving. Pistons can be sealed but it requires packing the chamber with grease which is messy and expensive causing service cost to increase *can be around $50 or more per first stage at service for the grease and extra cost for cleaning in the ultrasonic*. Sealed diaphragms are by far and large the preferred regulator for ice diving and nasty sump diving. Also nice for salt water since you can just rinse them off and there is no salt on the internals. Unsealed pistons require quite a bit of soaking to really get all of the salt out, as do unsealed diaphragms which imho are actually worse for salt water/cleaning than pistons because the caps can be a pain to clean out.
Balancing is one of the important aspects in CCR diving for some applications that require constant IP and sealed diaphragms due to the balancing mechanism are generally "over balanced" which means IP goes up as tank pressure goes down. This is the opposite of an unbalanced regulators trend, but it can cause problems in the volumetric flow of gas through the orifices and is a problem for some rebreathers. This is why you generally see unsealed diaphragms on certain CCR's. Poseidon has gotten around the sealing problem with their new MK3 and it's properly brilliant.
O2 use, pistons tend to hold up better to 100% O2 where you'll usually see some burn marks on the diaphragms. Not a big deal and don't know of any that have actually failed because of it, but you can get away with a bit longer of a service interval with pistons in general. Many still use diaphragms on their O2 bottles, but if I were choosing a dedicated O2 reg it would be a piston.
Size, most pistons can be made smaller than their diaphragm cousins. Poseidon has a small Mk3 for O2 bottle use that is one of the few exceptions to the rule, but if you look at something like the Scubapro MK2 or the Sherwood regulators they are super small, and diaphragms are generally a bit larger. I don't know of any diaphragms other than a couple from Poseidon that have the valve orifice on the bottom of the regulator, they generally come in from the side which makes them a bit bigger. This small design is nice for things like O2 bottles, CCR bailout, etc where you need as small of a profile as possible and the diaphragms stick out a bit too far.
Last for me is ease of adjustment for service. Up until the MK25 from Scubapro, most pistons required shimming the piston to change the IP where diaphragms are done by adjusting a screw with an allen key at the top. Super easy and convenient.