What I found much harder to adjust to, and wasn't expecting at all, is the shorter days in the winter. Is dark so much earlier- I very much miss seeing the sun in the winter...it is dark when I go to work, and dark when I get out.
Yep, I wasn't prepared for that either! The sun rising at 8:30 am & setting by 3:30 pm in the depths of December - ugh. On the other hand, June is brilliant - sun coming up around 4 am & it doesn't get fully dark until around 11 pm - midnight. Both HG & I live up north though (I go by Stuart Maconie's definition of The North in
Pies & Prejudice - The North begins at Crewe...though for some Londoners, it may begin at Watford Gap!).
The weather? It's much of a muchness really. Most of the year, temperature will be somewhere between 40-70 F, rain - some areas get more rain that others, meh. When it's chilly here it seems colder (I think) because of the dampness.
As for how different it'll be for someone coming from the US - all depends on where you're coming from & where you're going to over here. As for the over here bit, you'll get a different answer for someone living in Cornwall from someone living in Inverness!
I grew up & lived in Kansas for 33 years. Kansas gets both extremes - oppressive, tending to be dry redhot (landlocked) heat in summer, cold & snowy winters. I absolutely hated midwestern winters, and so moved to Tampa Bay, Florida, where I lived for about 6-7 years. Loved Tampa Bay weather & all that brilliant sunshine - for me, that's like the most perfect weather there is! Love it hot & humid in the summer, pleasantly warm 'winters', etc.
So when I moved to northern England, it was a real shock to my system - took me years to get warm, lol! And oh how I miss all that the brilliant sunshine (average sunny days in Tampa/St Pete of 360 days per year!). I guess I'm used to it here now - as used to it as I'll ever be, but I sure do miss long hot summers & the occasional thunderstorm wouldn't go amiss either. Up north, we're very lucky if we get a very small handful of days each year when the temperature exceeds 80 degrees. I feel like I have been cheated out of a proper summer pretty much every year.

And I look forward to warm weather holidays in the US, or places such as Spain or Morocco.
It was just my luck last autumn, DH and I went to the US for a holiday & family visit...we spent the first weekend of October in NYC - where it was 50s/low 60s & drizzly. Meanwhile, over here they were having freakishly warm weather of 80+ degrees & I wasn't here to enjoy it!