I imagine the ease of using old adventures really just comes down to the type of DM you are. If we reference back to the "do you fudge your rolls as a DM?" thread several months ago... those of us who do it (fudge rolls, adjust HP on the fly to make the fights more exciting/interesting etc.) probably have a much easier time running the modules because we don't really have to spend much time "converting" at all. We will just have the 1E/2E stats in front of us and just eyeball any adjustments we feel need to be made at the time the battle happens. For those mechanics they have that don't exist in 5E... we'll just quickly adapt a 5E equivalent.
Sounds a bit like me; I may well set the stats only when a monster enters combat, but I don't
fudge - I don't adjust the stats mid battle to make a monster harder or easier, just as I don't
"adjust" the results of dice rolls.