Using the right picture profile is tricky... For example, I've been working with some profiles such as Cinestyle and I too get similar results with the H264 exposure vs the raw... The reality of the processed image in LiveView is not the same as the raw footage being recorded to the card. Though I love looking at the Cinestyle picture profile compared to other picture profiles, especially in low-light... I will actually tend to shoot raw in Standard picture. Personally, I tend to dial in the Standard picture profile in a way that provides consistent exposure/noise floor results. Eventually, you'll be able to push the image as far as Cinestyle in post, but you've got to find the right pathway to the sensor and the LiveView.
The histogram doesn't lie... The Auto ETTR will push your shot right to the max without over clipping... You could technically continue to shoot with different picture profiles, but you'll definitely want to be zoned in on the histogram. Essentially, there are some picture profiles that truly boost the image to a great degree in LiveView. But, the data in the card is reading the information directly from the sensor. Keep practicing and stay true to the sensor readouts... They are there for you to push the limits. The LiveView simply serves as a constant unchanging rhythm featuring a dynamic range similar to a poor/standard quality computer monitor & television. Feel free to tune the LiveView to lean towards the results you most keenly require in post such as skin tones, black levels, and/or highlights.
Hang in there and keep up with the posts. Thanks everyone! Thanks ML Team!