Relatively worse, because (except in an extreme case <missed third strike> ) a K has no chance of moving up runners - other outs do.
A Strikeout also has no chance of causing a Double Play. There were 3784 baserunners erased in 2004 because of balls hit into play. Excluding Outs of choice (Sac Bunts), there were 3977 Runners advanced by balls hit into play in 2004 using ESPN's "Productive Outs" tracking.
Considering that losing a baserunner to a Double Play is actually a far worse event than any other Out event (due to the nature of causing BOTH an Out AND erasing a base), your contention that Strikeouts are far worse events than Outs created on balls hit into play is a non-starter. Also, considering the fact that many runners advanced on non-K Outs would have scored from their original basepath positions on the following event, it's a wash at best.
Sean Casey produced 18 "Productive Outs" in 2004. He erased 16 Runners already on base by hitting into Double Plays. Considering that those 16 GIDP erased gains already posted AND knowing that Outs are more valuable than bases, what we're left with is net negative event value.
Simply put, the Outs and Bases erased by Casey's GIDP's were more valuable to the Reds than the random bases gained by Out-event balls hit into play.