I already have the lens, M.Zuiko ED 12-40mm f2.8 PRO on EPL-5 camera body. I use this set-up for travel only.
I want to replace the EPL-5 with either EM-5 II or EM-1, because they are selling at the same price now. Also, they all have viewfinders, which I missed a lot with my current EPL-5. So which one is better fit for the lenses?
The E-M1 has a deeper hand hold and balances the lens better IMHO if you aren't going to get the HLD-8 for the E-M5 mark II (or a third party grip that adds some depth to the E-M5).
In terms of travel, while the deeper handgrip is better (IMHO) to hold heavier lenses, it does mean the camera takes a little bit more room in a crowded carry on bag due to the depth of the hand grip.
If you wear polarized sunglasses, both cameras have problems when you look at the viewfinder in landscape orientation with sunglasses on. I find the E-M1's EVF mostly usable to frame the shot (but there are spots on the EVF that I can't see due to polarization effects). My older E-M5 mark I and Stylus-1 have the same viewfinder and same problem. When I bought my E-M1, I did try out the E-M5 mark II in the store, I found it nearly impossible to use the EVF with polarized sunglasses. The E-M10 mark II and Pen F both have OLED viewfinders, which does not have this problem.
One thing to watch out for on the E-M1 is you do not want to set the diopter to a high value, since there are users that have reported that green blobs get etched on the EVF when it is exposed to sunlight with a high diopter set. If you normally don't set the diopter, there shouldn't be a problem. I don't recall if I've seen any reports of the E-M5 mark II failing in the same way.
If you are going to shoot video, the E-M5 mark II has better video support than the E-M1.
One thing that some people like/hate is the E-M1 only has a tilting LCD, while the E-M5 mark II has a fully articulated LCD. The fully articulated LCD works better if you are shooting in portrait orientation, and is perhaps better for video. On the other hand, the tilting LCD is better in tight conditions when you are shooting in landscape orientation (to use the E-M5 mark II LCD you have to fold it out to the left in order to to tilt it up/down.
The E-M5 mark II can do live view to a portable HDMI display, while on the E-M1 if you plug in a HDMI display, it goes immediately to review mode, and it won't let you take pictures. Both cameras can do live view to analog displays if you get the appropriate cable.