Hireling seems to me to be most potent in sloggy games. Take something like a Margrave slog, adding another card lets you hit provinces on off turns and makes your deck far more silver tolerant. Similarly when the curses are flowing that Prince or Ruined Libraries is something you can grab on your first $6 (maybe even T3) and then have a lot easier time getting back to $3, $5, or $6 for the rest of the game.
Slogs mean that you will not be drawing a bunch from somewhere else, that every price point is much more valuable (going from $2 to $3, $3 to $4 and from $5 to $6 matter a lot). Slogs also mean that you will get many turns of value, not just until you can draw your deck. Even with just a stock 2 silver opening, a Hireling raises your average hand to $5.5 while a Gold raises it only to $5.38. The gold does pay out a turn sooner, but the worse your deck is, particularly with lots of garbage curses, the better Hireling seems in early-mid game hands.
One very nice slog combination is with Quest. Hireling assures a gold every turn barring discard attacks which is not a bad hand when your deck has been nuked by Ruins or has been flooded by Coppers and Estates (e.g. 4er Amb wars).
On the engine side of the house, Hireling seems best when I am building an untrashed engine - if I plan on using a good bit of cellaring or some big draw like Envoy or Huntinggrounds, that extra card is worth a lot more given the odds of drawing dross each hand.
In general, Hireling seems much better when draw is very difficult to have going.