E-M5 vs. E-M5-II: clearly more moiré
Using a Bayer pattern sensor leads to moiré (false color) and to reduce the risk of that appearing in pictures an AA filter helps. If you have a mono-color (grey) scene with a fine-grained pattern, like a fine grille, there is a significant risk of ending up with false colors (a color pattern appears where there should only be grey). Unfortunately this happens a lot for me as quite a few of my pictures involve black accordions with (grey/black) patterns in their grille and on their bellows. I have needed to do moiré correction a lot more with the E-M5 II than with the older E-M5, yet the increase in sharpness in images between the two is absolutely negligible.
In any case, what is very important to note is that a lens that isn't "tack sharp" already acts as an AA filter. WIth most kit lenses you never need to worry about moiré as you have a "good" AA filter already. But with a sharp prime or a zoom like the 12-40 or 40-150 pro you do have to "worry" about the images being so sharp that the lack of an AA filter becomes apparent.
The AA filter in the old E-M5 is already rather weak. Here is a picture that shows the type of problem. I removed the moiré in ACR but you can still see artifacts from where it was. The pattern has to closely match the sensor resolution for moiré to start showing up. That's why it shows clearly in some picture and not at all in the next similar one that is zoomed in or out just a little bit more.
The grey panels at the back (near the center) showed a lot of moiré) and you can still see artifacts from moiré removal. The "streaks" you see are the evidence. The moiré was pretty bad before removal.
Here is an image with moiré from the E-M5 II. The moiré is visible (zoomed in to original size) on the grille of the accordion (almost in the center of the image). The fabric used in the grill has a uniform silvery pattern. The colors you see in the grille are not real.
Look at "original" to see the false colors on the grille.
Most of the pictures in my albums have had moiré corrected so I don't have many examples.