Along with position, how you play the OESD depends on two more things I didn't see above:

1. How many opponents are left.
2. How you got the flop.

I find it a lot easier to check/call and draw in multiway pots where folks are more tentative to bet since bets are expensive and are pretty likely to get called in at least one spot. HU, opponents will bet into you more when you try to check it down, and they often guess you're drawing and try to charge you for it.

For how you got to the flop, it matters whether you're in as the preflop raiser or as the flat caller. Because they have different ranges which will fit in with the board differently. As PFR, you're expected to have big pp's and AK/AQ type hands. As the flat caller, you're expected to have more small/med pp's, weaker Broadways, and sc's (depending on wide your flat call range is).

Consider this situation: LP raiser and a caller from the blinds. The flop comes JT5 raibow. Hero has KQ.

When Hero is the PFR, the BB knows he has a wide range, but the flop still favors the flat caller's range, and Hero is more likely to get called than on a Q52 flop.

When Hero is the flat caller, the LP cbet is likely to be a cbet flop, check/fold turn line. Hero can often check/call and get a free card for a second crack at the draw.

These may not be the greatest examples, but who's donking and who's cbetting matters. Donk bets and c/r's can really confuse some villains, so we can even use some of our OESD's to widen our ranges in those lines. In position, I almost always cbet as PFR since (if villain check/calls), I can almost always check behind the turn and get my free card if I want it. Like IOPQ said above: "I bet more flops than turns."