It's really hard for me to say where "home" is. Despite growing up in Ohio, it never felt like home. I just never liked living there and would beg my parents to take jobs in other states (they never did). I never felt like I fit in, either, and now that I've been in the UK for a few years it's feeling more like "home."
Since moving to the UK I've been to the US several times. I try to visit twice a year and each time I feel like I've moved further away from being American, but not exactly British. I'm just bobbing somewhere in the Atlantic. The first visit to the US after getting married, my husband (he's British) and I were in a shop paying for something when the clerk reached over the counter to explain what the coins were! I looked him straight in the eye and said, "I'm American," and he replied, "You don't sound it!" Even ordering a drink at Starbucks raises a few eyebrows, and a barista once said to me, "I could listen to you talk for hours!" I told them I grew up down the road and they didn't believe me. If you heard me speak, you'd know I was American. British people can always tell I am 100% American. But for whatever reason, Americans in America cannot.
My last visit to the US had CBP asking me all sorts of questions about why I live in the UK and if I would return (they even asked for proof of my itinerary). I'm a US citizen, and I only have a US passport (for now). I was shocked and hurt that as a US citizen I had to show that I would actually leave. And then for my flight back to London, the airline didn't understand what my BRP was! They wanted proof I was coming back to the US! It was just weird.
Returning to the UK, I'm always welcomed with a smile, and the immigration officers always welcome me back. They don't say "welcome home," but they say "welcome back."