Consider your use case. There aren't many situations where standard cruise has any advantage over adaptive cruise. If you're following another car at a more-or-less steady speed for a hundred miles, adaptive cruise wins hands-down. No need to manually adjust speed, disengage cruise, etc. This is the most economical state possible, as you are basically drafting them (at a safe and respectful distance, hopefully) with no manual intervention.
If you are working your way through heavy traffic, especially stop-and-go traffic, you may find adaptive cruise performance to be less than ideal—especially when some friendly driver cuts you off. The braking and acceleration behavior in close quarters may be a little more 'jerky' than you'd like. You'd be better off disabling cruise control entirely in that situation, as
@Edwards pointed out, as you can see further than one car ahead and plan accordingly. That said, adaptive cruise is still available to you under these conditions, whereas it would be unsafe to engage standard cruise.
If you're just cruising in the open country, with no other vehicles around, it really doesn't matter which one you use (as pointed out by
@U-235). The hypothesis by
@392DCGC that the acceleration profiles between the two systems are the same seems plausible.