Warmachine, and its companion game, Hordes, were made in the United States. Warhammer 40,000 was made in Great Britain.
The more I think about it, the more I feel like this explains a lot of the differences between the two games.
Warmachine's "Page 5" manifesto says up front that it is a game of aggression, of "challenging up the ladder" and kicking the crap out of your opponents, and it uses some creative metaphors for the crap-kicking process. It says it's not "permission to be a jackass," but that kind of sounds hollow when it also tells you to "go for the jugular and latch on like a rabid dog that hasn't eaten in days."
(Page 5 also says that it "doesn't discriminate between genders," but that is undermined by the Warmachine motto right beneath that paragraph: "PLAY LIKE YOU'VE GOT A PAIR.")
The Warhammer 40,000 rulebooks and art books like to talk about how "there is only war," and how dystopian the far-future fascist Imperium is. The actual game as written, though, is much more laid-back than its rival here in the States. The goal isn't to crush your opponent, but to "forge a narrative" alongside them.
Here's an excerpt from a sidebar on p. 14 of Warhammer 40,000: The Rules, called "The Spirit of the Game:"
Warhammer 40,000 may be somewhat different to any other game you have played. Above all, it's important to remember that the rules are just the framework to support an enjoyable game. Whether a battle ends in victory or defeat, your goal should always be to enjoy the journey.
Warhammer 40,000's rules are also a lot more open-ended than Warmachine's, and the game repeatedly encourages you to "add your own ideas, drama and creativity to the game."
How inclusive is each game?
Warmachine is a lot more inclusive in some ways. You can download the full rules for free on their website, along with stat cards for the most basic models. Privateer Press, the company behind Warmachine, has a very inclusive harassment policy for its events, and I have personally known it to threaten to pull advertising after a website published an over-the-top sexist and cis-sexist article.
In contrast, the cost to get started in Warhammer 40,000 is much higher, especially if you don't get one of the softcover mini-rulebooks that come in their Dark Vengeance starter set. (If buying one secondhand, make sure it's a 7th edition copy that looks like the one in the photo of Dark Vengeance's contents.) Games Workshop is reportedly a toxic place to work, with a CEO who prides himself on not doing market research, and they seem to think that only people who celebrate Christmas will buy anything from them over the holiday season.
The game's inclusiveness is hit-or-miss. Games Workshop rarely hosts official events, and has no harassment policy for them as far as I can tell. There's a lot less boobplate than in Warmachine -- practically all of Warmachine's female characters wear it, and/or high heels -- but it's damn near impossible to find 40k models of female characters at all. Unless you buy from third-party sculptors, or play Tau.
The difference is obvious
To me, it feels like Warhammer 40,000 is meant to be a hobby enjoyed by working-to-upper-class British men, with laid-back attitudes about competition and with access to lots of table space (at home or a wargaming club). Its management doesn't know or care how many women or minorities are buying the models, but some of their writers and licensors go out of their way to make 40k more diverse, and a lot of people collect the models without even playing the game.
Warmachine, meanwhile, plays like a competitive sport, just the way the "Americans" like it. Its writers and management are conscious of diversity, or at least of appearing to be diverse, but in practice their efforts often fall short because of the "hardcore" culture they create.
In my personal experience, I've actually been more offended by Warmachine's artwork and models than by 40k's, just because nearly all of their women have goddess-damned high-heels and boobplate. >_< And whatever Privateer Press' harassment policy for events is, I knew a jerkass in one store's Warmachine community who found out what one of my triggers was, and then deliberately invoked it on a subsequent day to get me to leave.
North American 40k players may be more intense than European or Australian ones, and I've even seen some conservative wingnuts unironically embrace its dystopian satire. But I also see a lot of laid-back, hobbyist types eagerly discussing the game and posting themed battle reports online. And my personal experience was of a more positive and accepting in-store community.
Which one should you play?
I have no idea. In miniatures games, it really comes down to which models you like, and what opportunities you have to play (with what kinds of people).
I'm personally not regretting getting into 40k, though. And there's a reason that the last time I picked up my Warmachine models, it was to use them as 40k proxies.