Hand of Midas - 1900 gold (500/1400). The cheapest farming item, it's 800 gold less than a Maelstrom, and offers an XP boost every few minutes. It provides +30 attack speed but overall is a very weak fighting item, providing no stats or damage.
Maelstrom - 2700 gold (500/1600/600). More expensive than a HoM, but significantly less than a BF, it provides +24 damage and +25 attack speed, as well as it's unique lightning proc. During 25% of your attacks a chain lightning will proc, causing 120 damage to up to 4 nearby enemy units. Upgradable to Mjollnir.
Battle Fury - 4350 gold (1400, 1200, 875, 875). 1650 gold more than a Maelstrom doesn't seem that much, but at this stage in the game, time equals money in a fairly serious way. The sooner you get your farming item, the sooner your gold boom can really take off. Offers no attack speed, but a substantial +65 damage, as well as health/mana regeneration.
As you can see, each item offers a different option. HoM is essentially just an XP booster, Mael boosts your damage output for faster farming, while BF offers fast farming and some regeneration.
These items fit with different heroes and situations - if you need a level advantage more than anything, and will have time to farm back the gold then you'll come out ahead. BF offers substantial farming speed that scales later in the game, and regeneration to keep you in the jungle. Mael offers increased damage output, and an upgrade that buys you a lot of attack speed.
There are a few potential reasons why I like Maelstrom so much on some heroes:
+ Attack speed scaling. Only Assault Cuirass and Mjollnir use Hyperstone as part of their receipe, and the nuts attack speed it offers. This works brilliantly when you have skills that work on % proc - for example Bash, Time Lock and Greater Bash.
+ Lower cost and more fighting power. I think the lower cost of this items make it more relevant early-mid game than the other two. That 1650 gold is almost enough to buy you a Drum of Endurance. This makes you less of an encumberance on your team and more able to carry your weight if required.
+ Flexibility. Similar to the last point, this item gives you options much earlier on about whether to farm or fight. If your team needs you to get involved, you can, if they don't, you can still farm effectively. Battle Fury pretty much commits you to a lot of farming as soon as you get 1-2 key components.
+ Works for ranged heroes. Although it's less likely to farm really heavily on ranged heroes, this is probably the best option since you can't use a Battle Fury anyway. Also works on both types of attack equally for heroes like Troll Warlord and Dragon Knight who move between the two.
+ Unique Attack Modifier (UAM) that doesn't totally block others. Unusually, you can still pretty much get another UAM to go with Maelstrom, it will only override the other if it procs, so you still get 75% of the other UAM's effect. Especially for a UAM like Desolator that doesn't need to proc every time to be equally effective, this is useful.
Some heroes that I usually consider Maelstrom on: (usually heroes with good base damage put poor attack speed, or heroes with % proc skills, or common Skull Basher carriers)
Alchemist
Doom Bringer
Dragon Knight
Faceless Void
Lifestealer (unusual)
Lycanthrope
Phantom Assassin (unusual)
Slardar
Sniper
Spirit Breaker
Troll Warlord
You'll probably notice that most of them are strength heroes, where the attack speed boost is especially helpful, and they're likely to be tanky enough to make full use of the Mjollnir lightning shield. However, you can also see a few agility heroes in there that can benefit too.
So would this convince you to give Maelstrom builds a try?
I think the whole problem with Maelstrom is that there is usually something that can be a better item.
True, if you're doing well, there is, but when you're behind in Farm and it's too late for Hand of Midas, Battlefury or Radiance and you need something to quickly get back on track, around the 10:00 -15:00 minute mark, is there a better Item then Maelstrom?
e.g. When you couldn't Farm up until that point due to a strong Offlaner, with constant Ganks from Supports and/or Mid, but your Mid Hero just got a Triple Kill and finally completed his 1st Core Item. This gives Map Control back to your Team for a while, long enough for you to Farm a quick Item that could let you get back ahead of the other Carry in terms of GPM.
I agree completely for supports...but then again I'm not a big fan of Hand of Midas on them anyway.
The argument I'm making in favour of Maelstrom is that it does give you more options early game - sure you'll want to go on to Mjollnir at some point (or it's a waste of money/space), but once you've got the first item finished, there's no reason you need to go straight on - for example for the price of a Battle Fury you could get Maelstrom and Drum of Endurance. It's also easier to change your mind half way - say you've bought a Mithril Hammer you could still make that straight into a Black King Bar or a Desolator easily.
Battle Fury only really gives you an "out" into Vanguard or Bloodstone (neither of which are that suitable on most carries). The other issue with Battle Fury is that although the health/mana regen gives you farming sustainability, that tick over is almost useless in a gank or team fight.
You could be most of the way to an Armlet of Mordiggian, Helm of the Dominator or Skull Basher by the time you got a Battle Fury - all of which give you far more effectiveness in fights.
I know there are definite arguments and situations where a Battle Fury will be superior (the farming speed and sustain are hard to argue with), but that Maelstrom should be considered a lot more than it currently is.
First, supports - Hand of Midas all the way, no questions asked.
For carries, it's a whole different story. If you were to take Maelstrom, you would do it because you want the Mjollnir and the 80 attack speed it brings. To take only Maelstrom (upgrading it only late game) is something viable, but unorthodox.
One huge con is the lack of damage and defense. 24 damage is something, but it's not much. Obviously this wouldn't be factoring in the attack speed and chain lightning, but chain lightning is based on luck, and while the proc chance is pretty high especially coupled with the attack speed, there are more reliable options.
It also does not give any defensive measures. It is an item purely focused on offense and thus it might leave some heroes being glass cannons.
If you were to take it as a "farming item" then you would want to take it early. However, if you take a Maelstrom early, besides gaining no sustainability like I said, you wouldn't really have that much attack speed to use the chain lightning to good effect.
I like Maelstrom, but I really wish there were more situations that I could genuinely feel that it was the best choice.
Also...
These items fit with different heroes and situations - if you need a level advantage more than anything, and will have time to farm back the gold then you'll come out ahead.
Grammar fail ;{)
Medusa I think has some Mjollnir based builds? Can see how that would work as she's ranged.
Phantom Assassin I'm not sure about...haven't tried it. You'd normally go BF for the extra damage stacking...but this build on her can be problematic as it means she can't gank effectively for quite a long time, and she's not a hard enough carry to be taking on the likes of AM with one.
Maelstrom doesn't offer the same damage total...but I think it kinda solves the timing issue, and the attack speed is a factor in her proc's - would proccing more often (and consistently) be worth trading some damage for? Aside from the Blink Strike hits, she's not the fastest attacker until she gets a lot of levels...and it also means she can be more involved earlier on.