Just grabbed my copy of The Book
Leadoff guy of an inning, so no one on base, no outs.
RE 0 outs, no one on base- .356
RE 1 out, no one on base- .182
ER 0 outs, runner on first- .704
So a strikeout to lead off an inning lowers run expectancy by .174 runs. A lone baserunner getting picked off with no outs lowers run expectancy by .522 runs.
So yea, I'm going with it being worse.