Depends on the situation. At 4am, with little or no traffic, they bend the rules a little at times. ie arrival on a STAR they use "at pilot discretion" and "decend via" a lot if there are no or little aircraft around. This comes from a friend that is a real world AA pilot.
Not only that, but when you have a CTR position open handling the Terminal area (as APP), they are going to be issuing that instruction anyway. If APP is on, there will be that line of separation there as to who issues the call.
At most RW facilities, that position is always manned, so they never will run into that problem. For us, it is different, because it will never be manned 24/7.
Me personally, I'll issue the crossing restriction first, as required by SOP/LOA between the TRACON and ARTCC facility, and then after they meet that, give the 'descend via' call. If there is little/no traffic around at that time, I might give the 'descend via' all. I say 'might', because of what the initial crossing restriction may be.
Example: the SUNST3 arrival into KLAS explicitly has its first crossing restriction to be at FUZZY at 16000ft, 250kts. So for that one, again, if no traffic is around at all, give the 'descend via' call. Same would apply with the SEAVU2 arrival into KLAX.
However, the RIIVR2 arrival into KLAX, the first crossing restriction is at GRAMM at/below FL210, and at/above 17000ft, at 280kts. That would imply that a crossing restriction is needing to be given. So I may issue two separate calls, or combine them:
'Cross GRAMM at xxx' (depending on altimeter setting), then when they cross GRAMM, issue 'descend via'..
Or they could be combined: 'cross GRAMM at xxx, then descend via'.
For the latter, Las Vegas TRACON does issue that at times for aircraft that may be high or to give a bit of leeway on the SUNST3 or KEPEC3. They'll say something like 'cross IPUMY at 11,000, then descend via'.
BL.
