I feel like you do as well, but a little reversed. I'm very logical and rational, and I hide my emotions often, so when they do come out (usually in an outburst, because inferior Fe is awesome like that) no one knows what to do. And on one hand, I'm lucky that most of my friends are introverted, but I'm the most extraverted out of all my close friends. So sometimes I do want to go out and stay out for a while, and they're like "Mehh let's be home by 9." And being an introvert/not outgoing myself, I find it awkward to ask my more extraverted acquaintances to go out and do something.Yes, I do. It worries me a lot. Sometimes I feel guilty about it, I blame myself for not appreciating their friendship. The thing is, I'm still waiting for someone who can understand me fully and know me like no one does. I'm sure I haven't met that person yet. Also, my friends are very logical and somewhat reserved, I often feel misunderstood and ashamed when it comes to showing them my emotions. They simply can't handle me the way I'd like to be handled. I can't blame them for that - the truth is I created a persona who is braver than me, livelier than me, more sociable than me, and I think that at this point of the relationship it's impossible to change my behaviour without them feeling confused etc.
I have things in common with all my friends, but not really most things. And I too feel like an outsider almost all the time, to the point where I am surprised if I'm not the one who is left out of things.I do have things in common with them, that's how we get to be friends, by bonding over common interests. The issue isn't whether or not we have shared interests because then I wouldn't befriend them in the first place, but more how I still manage to feel out of place, like an outsider. I don't think I've ever truly felt like I belonged.. which is why I seek one on one friendships. It diminishes that feeling of not fitting in, whereas in a group, it always ends up being the case.
Basically, I feel like while my friends know how I am in general, what I like and dislike, and are able to sometimes anticipate how I'd react to some things, they still don't know me truly.
Like @Aleksandra, what I long for is someone who understands me completely. Someone who knows me inside out and still accepts me and loves me.