Reddit reviews Fotasy 37mm Silver Screw-in Metal Lens Hood, 37 mm Silver Lens Hood fits Olympus M.ZUIKO DIGITAL 45mm 1:1.8 lens, for Canon Fuji Leica Leitz Nikon Olympus Panasonic Pentax Sony Lense

That's almost half the price, the Oly is a great deal for $180 IMO. I'd go for it tbh, but the subtleties might sway you one way or the other depending on what you'll use it for... So into the weeds we go...

The Oly has some field curvature which could actually contribute to what some describe as character but also seems to rob it of sharpness on the edges, when you're focusing on the middle of the frame anyway (if your subject is on the edge and you focus there it wouldn't be an issue).

The Oly may also filters a bit more UV since Oly is aware that they use a weaker on-sensor UV filter in their bodies, that may both contribute to less CA and/or pair better with Oly bodies. (wouldn't make a difference one way or another on a Pana body) It could also contribute a little to color rendering but it's kinda moot if you shoot RAW.

The Pana has little to no field curvature and OIS, if you're using it for portraits I don't think either of those elements really matter. Your frame is usually gonna be defocused around your subject anyway and you'd need to keep shutter speed up to account for subject movement. The OIS does come in handy for video if you were to use it on an IBIS-less body (I had a GM1 when I got it and now have a GX850).

I also like that it focuses much closer, the Pana that is, but that doesn't really matter for portraits either unless you're taking portraits of bugs, heh. It does make it a little more versatile, the Sigma 60/2.8 and the upcoming 56/1.4 also focus closer than the 45/1.8 tho not as close as the 42.5/1.7, which still yields the most magnification.

The CameraLabs review of the 42.5 compares them heads up and it touches on some of this, it doesn't explain the field curvature (tho LensRentals' has a good blog post on that) but notices the effect on edge sharpness (I still think Gordon had a less than optimal sample tho, but he said he tried several).

There's a few things I've been meaning to check out myself as far as CA on point light sources and bokeh, which might favor the 45/1.8, just haven't gotten around to it... The Pana has some cat's eye bokeh on the edges characteristic of a few Pana lenses.

I think the Oly is more round throughout. Honestly they're both great, you have to be pretty anal to notice most of these things (outside the two obvious pluses to the Pana which might not matter at all for what many will use it).

The Panasonic comes with a lens pouch and a hood too, so there's that. The Oly is part of an old series of Oly lenses (anything launched pre-25/1.8) that didn't come with those. I like this screw in metal hood on either just cause of how it looks and how compact it is, tho the OEM hoods are reversible (you also gotta take off a cosmetic decor ring on either to use them, bleh).

If you were gonna use it for something like landscapes or even copy work, the Pana has a clear edge in having less field curvature... I tend to use zooms for that myself but YMMV.

Edit: Whoa, that got long, hopefully it's more useful than hopelessly confusing. :s

Edit #2: Even more insignificant than everything else, I think the Oly is sold in black and silver whereas the Pana might only be sold in black in the US IIRC... I bought mine from Japan cause it was a little cheaper when it came out or something (in silver if you must know, my Oly as black, heh).

I always use a lens hood, both to improve contrast and to provide some extra protection for the front element. For the Panasonic, I use this lens hood from JJC: https://www.amazon.com/JJC-LH-46GFII-Metal-Panasonic-Lumix/dp/B00L4KR1ES. For the Oly, I use this metal one from Fotasy: https://www.amazon.com/gp/product/B0061GS1OO