I've recently watched Eternal Summer, Night Flight and White Night. Yes, all three are about homosexual relationships, but that's not really the point. The point is, that these three movies are different. They've got this more serious vibe to it. The storyline, the acting, the music, the atmosphere in it. More realistic. They differ from the average drama or movie.

I'm looking for more movies/dramas like these. And no, it doesn't need to be gay-themed. This 'thing' that I'm looking for in dramas and movies is something you often see in the slice of life genre as well. And many of them can also be seen at these artsy movie festivals. So ehm, any recommendations? 

I hope people understand me a 'bit. lol. Sorry if you don't. 
Since I didn't watch any of these movies, I hope I somehow guessed what you're looking for, so here we go:

LIFE
Days We Stared at the Sun
Tonbi
Usagi Drop
Zeni Geba
Kids
Holyland
Orthros no Inu

The last 4 are not so much realistic. Hope you like some of these :)
I also haven't watched any of those movies you mentioned, so I may got this wrong... but I second LIFE and Orthros no Inu

In addition,
Last Friends
IS
Yokoso Wagaya E
N no Tame ni

For the last two, I might confuse between "serious vibe" and "mysterious vibe" :D
Like other commenters I haven't watched any of the movies you mentioned, but Yakou Kanransha gave me a really different feel compared to other dramas (although I'm not sure if that's the feel you're looking for)
Thank you for the recommendations guys. I'll be checking them out asap. :) 
I haven't seen the movies you've mentioned, the only movie that pops into my mind that kinda fits your description is Hong Kong movie 'Happy Together'- directed by Wong Kar-Wai who is well known for his artsy, unique and visually compelling movies which differs from the norm. 

Happy Together