Consider a game where both Chapel and Steward are present.
- If the copper split is 4/3, is it better to pick up a Chapel or a Steward?
- Can you think of any situations where you'd pick up Steward if the split was 5/2?
I would (almost) always prefer Chapel.
Honestly, if Chapel's on the board, I will buy it before my first shuffle, almost no matter what. @ColinD's 5/2 hypotheticals all sound playable. (Steward/Fool's Gold sounds especially fun to me, especially if you can get another cheap card with +Buy.) But in every one of those cases, I think Chapel would work better than Steward. For example, in the Fool's Gold case, you can literally trash everything but Fool's Gold (and the Chapel) very quickly. If you can pick up a Market or two you'll soon buy out the Fool's Golds and that's the point when you want card draw. So now is the appropriate time to buy a Steward for that (unless there's a better option).
The thing about Chapel is that it makes your deck fast. If you open Chapel/Silver (and if you open with a Chapel you must buy something else that produces some coin or gains cards) and start trashing like crazy, pretty soon you'll be down to a 7 or 8-card deck, which means the good cards you've bought come up again really quick. It's fine if your non-Chapeling opponent has 2 Golds and you only have one if you're playing yours almost every turn! The situation is even better for terminal actions: a single Goons in an 8-card deck is better than 2 Goons in a 16-card deck because it'll come up just as frequently and there's absolutely no risk of collision. This is also why Chapel is so good at setting up engines: the engine cards are about the only ones in your deck, so they come up together every time.
Decide up front if you're going to use Chapel; if you are, buy it before the first shuffle. Waiting for an unlucky $2 hand defeats the purpose of Chapel: speed. With Chapel, you want to trash all the Coppers and Estates ASAP, and if you've waited a few turns and already bought several other cards you want to hang on to, you've already missed the boat on the Chapel.
When not to use Chapel:
Chapel is great because it can trash 4 cards at a time. Chapel is not great when your hand is small. If you've discarded down to 3 cards, your Chapel is now a crappy Steward, lacking the options that round Steward out into a useful card. Chapel is fast enough that expensive discard attacks (especially Goons ($6), but also Ghost Ship ($5) and Margrave ($5)) aren't too concerning. (Torturer even less so, just take the curse and immediately trash it.) But Militia and even Cutpurse can get in the way. This is especially true in > 2-player games where you have more than one opponent causing you to discard. If you almost always have a hand with < 5 cards, Steward is probably a better choice than Chapel.
Jack-of-All-Trades can also compete with Chapel. Chapel will be much more effective at setting up an engine, but Jack is faster as a modified Big Money strategy. (I'm pretty sure about this. It has probably been simulated, I'll look around later for results.)
@User1873 astutely pointed out that you need to consider available card-stealing/trashing attacks in evaluating Chapel. Thief, Noble Brigand, Pirate Ship steal/trash treasures and make a Big Money + Chapel strategy riskier. A lucky attack or two could leave you in the unfortunate situation of needing to buy Coppers to afford a Silver! Any heavy trashing increases your treasure density so much as to make treasure-stealing cards very appealing. Be cautious of trashing too much when the stealing cards are out there. This isn't so much of an issue, of course, if you're building an engine with lots of action cards. Like the drawback of discarding attacks, the risks are exacerbated if several opponents are using stealers.
It depends on what other supply cards you want in your deck and what attack cards are present on the board.
Chapel is powerful because you can use it trash your entire starting deck in a couple of turns. The downfall is that in the short term, for those couple of turns your buys will be either non-existent or will be very low. If you buy a chapel, do not count on getting to $5-6 early. If you absolutely do not want coppers and estates this is the card to get.
Steward is a little bit more rounded. Its trash curve is slower and will involve you having to pick between trashing or playing it for one of its other options each turn. This can help you get to $5-6 sooner which can be extremely powerful.
strategies for 5/2 opening steward buy: disclaimer, these are heavily supply specific and were generated off the top of my head:
Steward + fools gold sounds pretty fun. Use the trash early to trash non-fools golds, leaving u with 2 cards that can hopefully buy you more fools gold. Later in the game, use it for the draw power to draw fools gold.
Another situation I might consider is steward + squire if there are good attacks on the board. The first couple turns, you should trash coppers and estates while picking up more squires. then start trashing them and picking up attack cards (this will work especially great with cultist).
Chapel is obviously better for trashing, but Steward has many other uses
The ability to trash down quickly is very powerful, and good Chapel play generally is aggressive Chapel play, destroying as many cards as possible in the first few. But Steward is so flexible, that it is well worth considering in many decks.
If both Steward and Chapel are available and I have $3 to spend on the first turn, I would have to look carefully at the rest of the board before making my decision. For example, if Mountebank is on the board and there isn't huge engine potential, I would take Steward/Silver instead of Silver/Chapel. The effect of Chapeling down your deck will be mitigated if your opponent is handing you two junk cards every turn.
With Steward/Silver, if you draw the Steward with four coppers in the next shuffle, take the Mountebank. if the Steward comes up with 2 estates and 2 coppers, then just trash the estates. There's a lot of flexibility.
What about the 5/2 split?
If both Chapel and Steward are on the board and you open 5/2 ... the thing is, it's harder to justify taking the Steward over the Chapel because the comparison will be
[power 5 card] + [Chapel]
[Steward] + [nothing]
Most board have 5-cost cards that are very powerful, and by themselves they might be preferable to Steward.
If Dukes are out (especially in 2 player games) I would consider Steward better than Chapel for sure. I would NOT get a Chapel in a Duke game because Copper isn't bad at picking up Duchies or Dukes. The Steward remains a solid choice because you can trash your starting estates, or use it for +2 Cards to cycle faster, or more likely use it for +$2 to get enough cash to purchase a Duchy or Duke later on. In 2p games, I would say that 70% of the time when Duke is out you want to go for a Duke strategy over Provinces.
If you interpret the question a little more broadly, it is definitely better to pick up Steward over Chapel if Hunting Party is on the board. However, I would still open Hunting Party / nothing, and then get Steward in turns 3 or 4. Hunting Party decks don't need much trashing, and the Steward will suffice in getting rid of the starting estates so the Hunting Parties will run much smoother.
To play this Hunting Party deck, you'd buy LOTS of Hunting Parties, 1 gold, 1 silver, 1 steward, and once you have a critical mass of Hunting Parties plunge for Provinces. But you do NOT want diversity here. Steward will act as Trash 2 until the estates are out, and then switch to +$2 to get Provinces. (1 gold + 1 silver + 1 copper + Steward = Province)
With that said, Steward is an average payload for a Hunting Party deck, and more often than not there will be a card better than Steward out there to use.