It can be tough to both make sure you get the strike and get the out at second. In terms of possible trade-offs, if you could almost always expect to get the runner at second, trading a strike for an out would generally be a pretty simple decision. If not, there would seem to be a lot of factors for the catcher to consider in deciding whether or not to hang in there just a hair longer for a better chance of getting a strike. A non-exhaustive list:
1. Game situation – score, inning, number of outs, how important is the runner at first?
2. What is the count? If it’s 1-2, getting that third strike looks like a pretty good deal.
3. Speed of runner.
4. Pitcher’s ability to hold runners; delivery time to the plate.
5. What pitch is the pitcher throwing when the runner goes – a fastball or a big slow curve?
6. Pitch location – is it a fastball right down the middle that the umpire can’t possibly miss, or a pitch on/just off the black.
7. What is the catcher’s throwout percentage?
I think most coaches have priorities/preferences. For example, several years ago I met a young catcher in the Atlanta Braves farm system who said that the organization-wide rule was essentially “make sure you get the strike, then worry about throwing out the runner.” However, it would seem that even with clear team/organization preferences, there is still some room for judgment by the catcher, taking into account the specifics of the situation. Presumably, the older, more experienced the catcher, the better he’ll be at exercising his judgment.