ZAB Controller expressed concern regarding the confusion reference the 'descend via' phraseology and the apparent uncertainty by both controllers and flight crews as to the required/expected published airspeed/s.

Narrative

An A321 came over from ZLA60 assigned 300 KTS or greater. Published speed at SCOLE is 280 KTS. I gave a CRJ9 the 'descend via' clearance with the 25L transition and told them to comply with the speeds starting at HYDRR (published 250 KTS); pilot read it back questioning what I had given. I said it mostly the same way; but gave comply with the speeds from HYDRR inbound. When the A321 was past HYDRR; they were still showing 450 ground speed. I asked them if they were at 250 KTS; they said they were slowing. The next aircraft on the arrival was the CRJ9; they were also assigned 300 KTS or greater. I gave them the 'descend via' clearance without any other guidance; expecting them to comply with the SNRRA speed (265 KTS) and the rest. The pilot subsequently asked me if they needed to comply with the speeds; I said yes. Even though our expectation as controllers is that the 'descend via' cancels any previous ATC assigned speed; the pilots still aren't sure what to do. Recommendation; our RNAV procedures are fairly simply when we have a single stream or aircraft in isolation. However; you start mixing in turns; sequencing; or speed control; and things get very confusing for both the pilots and controllers. Training was extremely poor; worse it would appear for the pilots than us. Phraseology needs to be addressed and I believe this is a national systemic problem and should be addressed.