I like to go back and watch a video like that a bit more closely a 2nd time, pausing at certain points. One place that got my attention was when they were comparing resolution and shooting that sign post.
For a brief moment they had a side by side (split frame) comparison shot of the both lenses at f 2.8. For me, the Panasonic seems just a tiny bit sharper, but probably nothing that an adjustment in post couldn't fix.
However, in that same frame, if you look at the bokeh of the out of focus background area, I definitely prefer how the Olympus looks, with a softer, gentler bokeh.
I do a LOT of close focus telephoto shots at f2.8 specifically to get that nice bokeh, so that's an important trait for me, and while this particular shot wasn't designed with that in mind, for me it gives the edge to the Olympus.
But, in the final mix of things, I think there are quite a few differences in these lenses that will sway somebody one way or the the other, like size, weight, extra wide angle, extra long zoom, built-in stabilization, etc.
It's certainly nice to know that which ever way you decide, you're going to end up with a mighty fine lens.