I will throw in my 2 cents as a long time Olympus shooter and owner of both the EM1 and the EM1 II.
The mark II is a big improvement over the EM1 in several ways - better noise control, quieter shutter, and has 2 SD card slots.
In either case, pay for the good glass. I have the F2.8 12-40MM, the 2.8 40-150MM, the F2.8 7-14MM, and the F1.5 45MM lenses and love them all.
Need shallow depth of field? The faster glass helps, but with the crop factor, F2.8 is not the same on the Olympus as on a full frame (not as shallow).
Solution? Use a longer lens and get further back. You can get great portraits with the 12-40, better with the 45, and really control the DOF with the 40 to 150.
Shooting lots of landscapes? The DOF challenge is in your favor here since you can use a larger aperture and higher shutter speed (don't ask me to get technical,
but think of how much more depth of field you get with a small sensor phone camera compared to a full frame).
The lightness is definitely good, but good glass weighs more no matter what, so if you have been shooting a Rebel kit with kit lens and you move up to what I have, you might not notice
the lighter factor. However, comparing the EM1 II to a higher end DSLR with quality glass, you will not be disappointed.
You can check out some shots I have made at
www.RonD-Photography.SmugMug.com - all photos were shot with Olympus cameras (E330, E620, PM1, EM1, EM10, and EM1 II).
On my wall I have 24"X30" (approx) photos from each camera and am happy with all of them.