Are there any different in using camera in manual mode vs aperture mode plus exposure compensation? This the same according to dynamic range or maybe something other difference?
Auto with exposure compensation (at a fixed ISO) can give you the same lighting levels as manual, unless you want a very under- or over-exposed image (according to the meter in the camera).
What it's unlikely to give you is the same combination of aperture and shutter speed. You can get this combination by using program (P) mode, with exposure compensation and program shift. This can be a little fiddly but I use it on occasion. Program shift keeps the same total light level, but allows you to trade off shutter speed vs. aperture on a dial. Many auto modes even set the ISO for you - though on SLRs there's usually an auto mode that doesn't.
The dynamic range of the sensor is fixed. Optimising the amount of light falling on the sensor allows you to use as much of it as possible. Saving as raw means it's kept when you save the file, while jpegs throw away some dynamic range.