Second, in four-player games, most attacks get a lot stronger. You can afford to play attacks that normally would be quite weak - Thief springs to mind, naturally, but say you have Militia on table: in a four player game there's three chances for it to be played before the BM+X player gets in, and that will slow the game down enough to give Engines more of a chance.
Wait, is it true that "most attacks" are stronger in 4p? I thought many of them were quite a bit weaker, at least in the sense that you get less marginal benefit from using it in a game where other players are using it. That is, in a 2-player game, if you don't buy Militia or Witch and your opponent does, you're the only one who's being attacked; in a 4-player game, if you're the only one without Militia or Witch, everyone is still going to be playing with 3-card hands and curses anyway.
I would say the marginal benefit of playing an attack gets weaker, but nevertheless you are usually under stronger attack, so it's more difficult to play BigMoney.
It depends on the attack type. Gain type attacks: thief, jester, noble brigand, and pirate ship (gain tokens) are better as you have higher odds of getting something good. Cutpurse gets much better as it stacks heavily; dropping from 5 to 4 is harsh - dropping from 5 to 2 is brutal. Torturer and rabble also get better as stacking between multiple plays per round makes them much harsher.
On the flip side, many attacks stack very poorly. Most discarding attacks, aside from cutpurse and bureaucrat, have no attack value after the first two plays of the attack on a round. Bureacrat is normally, pretty much much fails to stack as well because odds are rather low for all the pieces (two or more attacks hitting two or more green cards). Fortune teller does not stack at all and even spy, scrying pool, and oracle also tend to lose value as the attack is less and less likely to turn down good cards as it is played more times each round.
Card trashers - sab and swindler. Really seem about the same between 2er and 4er. Yeah, your odds of hitting someone's key 5 or whatever goes up, but you also have improved odds of having one lucky guy who keeps getting his silvers whacked.
Cursers tend to get weaker as game size goes up. Losing the curse split 10 - 0 is much worse than losing it 14:9:9:8.
All of this brings about a very important point - unlike in 2er, in bigger games you are often better off mitigating the damage than playing the attacks yourself. All the other players going ghost ship? You are almost certainly better off buying a smithy instead; they will most often play 4 card hands (after ghost shipping) and you will play 5 (after playing smithy). Likewise, going for an upgrade instead of witch will often be the better long term move (certainly almost always better than getting a second witch in 4er) - you can trash an extra curse each time through the deck and still enjoy advantages like better odds of upgrading late game duchies.
I have to say that attacks tend to favor big money in a lot of 4er setups. It is just as hard, if not harder, to make engine progress when you have attacks flying around. Too many workable engine components cost 5 or more and 5 is difficult to hit when you are tossing cards into the discard or have curses gumming up the deck. For big money/draw your price points are 3, 6, 9 and 5,8,11; the former does not care so much about attacks, you will hit a lot of 3s and eventually a good number of 6s. While an engine player will quickly exhaust whatever 3s or 4s are out there, silver never runs out.
The best engines for beating BM/draw are green tolerant engines. Xroads is phenomenal for this. Just pile on duchies, cross roads, and any cantrips/villages you like under 5. Other options include sifting engines (embassy works very well here), golem engines, and top decking engines (e.g. KC/scheme, watchtower/IW, and inn abuse engines) - you will need to green sooner in 4er and your engine needs to be able to cope.
Another option to beat BM/draw is an eternal game. VP chips are good, but outside of a few corner cases (e.g. watchtower/goons) goons engines run into the problem that piles deplete so quickly you can't milk the goons for points for too long before the game ends. Bishop and monument, however, can rack up points forever (in the former case you need to make a call if you want to deplete the provinces for more points or leave them to let the game hang longer).