If nuclear war divides the US into two warring factions based on (arguably) the two most enduring cocktails—martini drinkers and Manhattan drinkers—the Manhattan drinkers are going to be severely outnumbered.
I'll admit I'll probably side with team martini when the end times come, but that's not to say by any means that Manhattans are an inferior choice. I make a decent amount of both here at home. However, while I'm typically pretty set in my ways with how I like my martinis, I'm less set in stone about how a Manhattan should be built. I'd like to think that there's a huge degree of flexibility in the cocktail itself, and I think bartenders seem to agree.
The basic components of the Manhattan are whiskey, sweet vermouth, and bitters. In terms of the whiskey, you can choose a bourbon, a rye (either high-rye or “barely legal”), or even scotch if you want to turn it into a Rob Roy. The sweet vermouth can be substituted in whole or in part with various Italian amaros for something more herbal and bitter, and if so, other liqueurs can step forward to do some sweetening.
As for the bitters, you've got a staggering variety to choose from, including orange, rhubarb, Peychaud's, and Angostura, to name a handful. In any case, there doesn't seem like there's a wrong answer with how you assemble the components, so long as you do it thoughtfully.
What I'm saying is that there's a lot of permutations here. Where the Martini seems “off” if something's out of whack—a quality I'd attribute to the gin as a base spirit—the whiskey base is bold enough to absorb all of the various secondary flavors. For that reason, I'll give you not one, not two, but three different recipes to illustrate a few ways you can take the cocktail for totally different experiences.
2 oz Rye
1 oz Sweet vermouth
2 dashes of bitters (Angostura would be my choice)
People are generally more accepting of a 2:1 ratio of spirit to vermouth in the Manhattan than they are with Martinis, for whatever reason. I would tend to agree with drinks guru David Wondrich that using Bourbon throws off the balance of the drink. If you need a whiskey to make cocktails with, a go-to Rye like Rittenhouse or Crown Royal Northern Harvest would be my choice. For vermouth, use something good, since you're using more of it in the recipe. I like Dolin and Noilly Prat.
The Little Italy
2 oz Rye
3/4 oz sweet vermouth
1/2 oz Cynar
No bitters here, since the Cynar is giving herbal flavor out the wazoo. If you've never heard of Cynar, it's an amaro made from a number of herbs and plants, including artichoke of all things. It sounds disgusting, but a $25 bottle of Cynar deserves a home on your shelf if you're a Manhattan drinker. Usually when I make this drink for people, I say "Just drink it and tell me if you like it. Then I'll tell you what's in it." Kind of like the way that you get kids to try Brussels Sprouts. The Little Italy is brooding, full-flavored, and wonderfully balanced.
The Heart of Oaxaca (Credit to Dennis Schafer)
2 oz mezcal
1 oz sweet vermouth
5 dashes mole bitters
Here, mezcal gets subbed for the rye, and mole / Aztec chocolate bitters add depth and sweetness to compliment the vermouth. Is it still a Manhattan? That's debatable now that we're really monkeying with the formula. However, it is unusual, delicious, and a great example of how the same basic formula can be modified and still generate well-constructed drinks.