Thing is there are a lot of things that happen between 1776 and now In the US.
Where else would they go?
I think BNA expands beyond the Appalachians, but I imagine far less multiethnic immigration occurs, more along homogenous lines - like Australia and New Zealand (primarily English, Scottish, and Welsh). Australia did not really permit mass immigration from Southern and Central Europe until after WWII. Canada of course had some multiethnic immigration, but I think it would be a lot less pronounced.
Colonial America was already multiethnic. Around 75% Anglo the rest Germans, Swedes, Dutch, French.
What I think would be the change is, it retains its protestant migration patterns (Irish are likely exempted due to being in Britain).
So the Ellis Island migrations would likely be retconned at least in magnitude. I mean there has been Italian or even polish migration since day zero, Columbus. So America already lost its opportunity to be 90%+ Anglo-Celtic like Australia and New Zealand by 1770.
On the other hand, during the early part of Industrial Revolution Britain led the way and the US had to indulge in a lot of industrial espionage or use of British expertise to launch its own new style economy. It's often said that British foreign policy is basically pragmatic and that it dealt with many issues of the era by bending rather than breaking, so maybe if there had been unrest but no war, the British may have put more emphasis on developing North America.
Instead of the US having to steal UK secrets, they already have access, and a larger industrial base to build from (England). So industrialism in the US would be supercharged.
The butterflies are huge given the 250 year window for change, but based on comparing the modern US with countries that remained British for longer like Canada, Australia, NZ and the UK itself, a US that remained British, compared to OTL US would likely:
Pros/better developed British North America:
- Likely to have better and universal healthcare
- Likely to have less poverty and homelessness
- Likely to have less violent crime and gun-related crime
- Likely to have more social equality
- May have better public transport infrastructure (although still behind Continental Europe and East Asian nations)
- Probably would have abolished slavery earlier and less violently
Cons/less developed British North America:
- Less immigration and diversity, food/cultural options might be more limited
- Possibly less innovation and economic dynamism
- OTL world leading and dominant economic/soft power sectors like finance, information technology and media would look very different or be butterflied away. London remains the leading financial and media centre, as for the tech sector, who knows.
Areas up in the air as to whether a British North America may be better or worse than OTL US:
- Education - both are strong OTL
- Taxation - would be higher, for better or worse
- Environment
- Race relations with African Americans and Native Americans - probably just as bad based on experiences in the British dominions
As it's an entire continent, it can't really replicate England, so it's naturally going to be different. Public transport outside of cities aren't practical in the same way the smaller British isles are. Or gun culture, which was a very colonial thing which exists in 🇨🇦🇳🇿🇦🇺, and the gun crime aspect is more 20th century related.
As for migration patterns, they'd be less variety. But foods and cultural options wouldn't be limited at all. People have access to recipe books, or foreign entertainment like anime or K-pop or french music etc.
Ironically taxation would be less, a small island might be able to have an empire, but it certainly can't tax them. I think tariffs as a trade barrier are more plausible, although correct me if I'm wrong 👍.
Environment or more specifically nature would be less stressed and used, as the population would be smaller with different migration patterns, there is only so many people available to migrate.
Plus, I would also see a much larger South Asian population. Not to the degree of the various Caribbean islands or Guyana, but I could certainly see a large number of Indian* indentured workers brought to the south.
(I am aware that the US tried something like this IOTL, on a more limited scale.)
*and possibly Malaysian and Chinese too
Do you know if Newfoundland, Canada, Australia or New Zealand have that migration pattern pre-1950?
From what I've read, Indians that wanted to migrate to Canada went to US, and that was where the various plots and mutinies in the British Raj were created.