Yes, the BMPC has a better codec. Yes, it has greater dynamic range. Yes, you get a flatter image from i than the GH4. And yes, the picture is better for color grading. But that doesn't mean you'll end up with successful shots. First of all, the fact that the shots are easier to grade does not mean you'll end up with a nice color, you actually have to be good at color grading(duh). Second of all, there are ways to get a flat enough image from the GH4 so that you can grade it properly(even though you only have a 4:2:0 8-bit solution, without the Atomos Shogun). Third of all, the dynamic range of the GH4 isn't that bad(yes, the BMPC's dynamic range is a bit better). And fourth, but not least, GET SOME GOOD F*CKING GLASS. The camera it self won't give you a nice picture without a nice lens. Oh, and don't forget, getting a good camera with a good lens doesn't necessarily make you a good cinematographer/grader/director/editor/whateveryouwanttobe. It's all about the person standing behind the camera. jk it ain't really like that(although it often is). btw as mentioned the battery life of the BMPC really blows, and since it's such a small thing it'll heat up pretty quickly. Be prepared to buy a couple of hundred of batteries, if you go for it.
Conclusion: Get a RED Dragon with a Carl Zeiss lens that costs at least 20 grand, a 20 grand rig, and you're good to go. Or you can buy the GH4 and be happy with it.
I hope this helped, although it probably didn't. If you want to hear a professionals view on the BMPC and the GH4, check out Philip Bloom. Great guy, great reviews.
Cheers gapers.