I have had a bunch of different glasses, from cheap to prescription. While being polarized seems like it would be a simple yes / no or on / off type of thing - it unfortunately isn't. Adding mirrors to the equation adds another level of complexity. It also adds another layer of light dilution / image degradation.
The color of the lens has an impact on how well the reflections are quelled by the polarization process as well as how the actual light transference works. I, for example, prefer an orange / yellow lens for most things, second to amber/copper. Unfortunately, polarized yellow does not have the same properties as polarized grey does. 1:1 polarizing yellow sucks compared to polarizing grey tints. Suck's so bad that I returned a pair of prescription yellows and got standard grey...same tech, same glass, same prescription, same everything except tint color --- and the difference was night and day. I wear those grey's daily as driving glasses and on the water if it's a bright day and I wont be fishing in a lot of shade or doing much sight fishing.
If I am going to be doing more under trees, in shade, or sight fishing etc, then I wear my copper costas. I know, I haven't spoken to mirrors yet but I'm getting there, lol. I personally like a lighter lens. I don't want UVA/UVB but even lightly tinted lenses protect you from that. If you add a mirror you are always making the lens a shade darker. Maybe not much, but it is something to consider if you ONLY have one pair to wear. I love my grey's for 90% of what I do with them, but if I am trying to see under trees in full sun, they are just too dark. Because of that, I usually just wear the costa's when I fish. Before the "Copper" Costa's I used exclusively amber colors for fishing (for the same reasons), regardless of the brand.
If I were an open water fisherman, like saltwater for example - I would probably add blue mirrors, and probably have them over a grey tint. But, I end up in a lot of different light conditions, cloudy, shade, early, late --- all those hurt grey, imo. I want to have as much light as I can get, while still having good polarization so I go amber/copper with no mirror. The reflection of the specific wavelengths does add a little contrast. Reflecting green away from green, blue from blue, and any other color you choose to mirror with. The thing to consider is those colors reflected away, change what you see. The tint absorbs colors, the mirror reflects them --- so together you get different results.
Having said all of that --- 99% of people wont care. Buy what you like the look of, and accept that whatever color shift you get is what it is. After a few minutes you wont really notice it unless you have two pairs side by side and swap them back and forth --- then the difference is rather noticeable. Just a blue vs green tint over amber makes a big difference side by side.
Here is a list of what the impact of colored mirrors actually has --- but until I can really see them side by side, I go mirrorless, but I know of bunch of people who love their green mirrors on small freshwater and blue on open water.
Blue mirror - shifts colors towards yellow
Red Mirror - shifts colors towards blue/purple
Green mirror - shifts colors towards rose/pink
Gold mirror - shifts colors towards green
Yellow mirror - shifts colors towards blue/green
Teal mirror - shifts colors towards magenta
Silver mirror - tends to darken without much shift in color
Amber/Copper tint tends to shift the perceived color range towards green and reds IIRC --- I know I like that better than what the greys do overall. And I seem to remember something about reds helping with depth perception, but one would have to look into that. But, you can see the green mirror will shift slightly towards the reds, which is what the amber color lenses do, so you probably will get a little more contrast with the green mirror.
However, if I am looking at a cheap pair of glasses, I personally would avoid mirrors. While a good mirror coating with help protect the lens from scratches, etc. a cheap layer will scratch more easily as I understand it. Also, consider the impact of the tint vs the mirror. Grey and amber tints usually blocks like 10-15% of light transmission, tint 2%. (roughly of course) So the tint you choose is much more important than the mirror, and unless they are side by side you will probably never notice the difference. If you like a little darker, maybe a bit more contrast - add the mirror. If you like a little more light for seeing in low light, into shadows etc, skip the mirror. If you don't know / don't care - pick the look you like and rock on!