Probably worth talking about HDR a little more in the context of m43 vs full frame. What AM is referring to there is HDR capture, but HDR just means "High Dynamic Range", and one way to achieve this is to do an HDR capture, that is, say three shots with different settings, one exposing for highlights, one for midtones and one for darks. The clever software then smashes them together to get the "best bits" of all three. The resulting image often looks ultra vivid and unreal because that isn't how you see it in real life. The shortcoming of any sensor is that their dynamic range is less than the human eye, around half the variation your eye can cope with at a time.
There is also the possibility of creating an HDR image in post processing, I normally refer to that as "Qasi HDR" because with HDR capture, you store more information, post production HDR is software driven. Where this plays into the conversation is where you make mistakes. Say for example you screw up in taking the image, and under expose badly - this is an instance where it makes a difference if you shoot RAW or jpg - If you shoot raw, you have the option of post processing HDR which is more successful in my experience than simply lifting the shadows (although that is clearly is a key part of it). You certainly can also HDR process a jpg, but I've found that it is more successful working from RAW.
Here's an example of one I took earlier, got wrong, but was able to make reasonably acceptable with that technique. If you look at the person seated on the right, you will see their face has an unreal look about it, the "HDR" process has kept some deep shadows as well as lifting the exposure on the rest.
So, if you started with a FF which has a greater dynamic range, you also potentially can fix screw-ups better.