Hey, Jokin.
I'm not a expert, so this is my personal opinion.
I think they have the same meaning, too.
But, 「~へ行く」sounds more formal to me than 「~に行く」.
Personally, I usually use 「~に行く」in daily conversation. But when I want to speak more politely, I tend to choose to use 「~へ行く」.
Also, I think 「~へ行く」is more literary rather than colloquial.
I feel like I see 「~へ行く」more often in written form.
I hope it will help. :)