Two United States - one that is based on New York, Pennslyvania, New Jersey, Delaware and New England which is very industrial, very commercial and outward looking and a more rural US covering the more outright Democratic-Republican parts of the country starting from the Left Bank of the Chesapeake and the northern Appalachias and heading south down to Florida.
If you think about it, these were very different places in a lot of different ways, demographically, financially, culturally and politically. Some of the states were less explicitly or ambiguously Patriot prior to the Revolution. If a different approach to the relationship was attempted, lets say the Westminster Government made the decision to offer meaningful concessions and been a bit more flexible in its views, if they had chosen to negotiate separately with each colony and offer different packages of concessions depending on what colony it was and how Loyal it was perceived to be, say offering much to the South but less to the North, different outcomes might have happened. Its also possible that the compromises made creating the Constitution from the husk of the Articles of Confederation failed and two states were created instead of one United States.
This means that we could explore some of the issues inherent in the US's 18th and 19th century development, without the ickiness of having to deal with the Confederacy and Union loss or draw during the Civil War. It's still VERY icky, given the presence of slavery regardless, but it means that we don't have to construct a timeline where the Confederacy actually win despite the odds. The South would at least theoretically be more exposed to British anti-slavery measures due to their relatively weaker position to resist, with significant economic and social consequences there. For example, the issue of freeing slaves and free soil politics might become more important in a predominantly rural state far more quickly, especially one that is keen for cheap agricultural labour and concerned with its borders. This also opens up issues around the job market and Freemen and poor White Southerners competing and whether Sharecropping becomes the Southern model far sooner potentially or whether they clamp down ever harder and find making trade deals more difficult as the British move into enforcing the end of slavery, potentially sooner given these issues are likely to be highlighted simply by the increased political and diplomatic engagement with a Southern US due to a divided state.
I would be unsurprised if the constitutional frameworks of the two new Americas are markedly different, given the compromises that go into making the US Constitution to support the different interests of what would be here two different sets of newly minted states would be changed. I do wonder whether the South might take on a system far closer to the British one than the very Classically influenced version, no matter what state Madison, Monroe and Jefferson came from. If the other lot of, what they might like to see as jumped up, money-loving Yankees are trying something, they might not want to do the same thing, or vice versa. Mostly rural nations tend to be a little less radical as a whole. Where the capitals of the two nations would be is also up for discussion, would the North end up in New York and see a consolidation of economic and political power on one city? Where would the South choose to site their capital? Somewhere in North Carolina is roughly in the middle of the proposed nation, but would Richmond grab all the glory as the dominant state or would Virginian leaders think the better of it for strategic reasons?
It's also possible that with a different Revolution where let's say there is a case by case basis negotiation going on, less colonies rebel and less Loyalists leave for what becomes Canada, which changes their temperament a lot too, potentially ending the development of Canada as a loyal Dominion given the geography and unpredictability of Quebec, separating the Maritime and Atlantic provinces as it does from the rest of Canada.