Mirrors are typically much less expensive than their bigger aperture brothers in the same focal length and, after having both, the traditional lens beats the mirror hands down. Images made with mirrors are softer, have OOF donuts and contrast is noticeably less than a traditional lens.
I doubt you will ever see a pro wildlife or sports photographer with a mirror.
Mirrors are initially fun to play with but I tired of it quickly and it went to live elsewhere.
Doughnuts are more of a specular highlight issue. But out of focus lines will look doubled and this is often described as bad bokeh. Although in grass and foliage I find it in character. they are F8 usually so you change the shutter speed or use filters or different iso film. The mirror lens is Much lighter. the mirror lens is less contrasty But jumps into focus. The inside element is a replaceable glass and comes clear, yellow, orange, red and polaroid. I rather like my Sigma 600mm in Contax mount on safari as the decreased contrast softens the harsh shadows of the African sun.
But I am an amateur.
it cost 90 dollars and I like it better than my fixed zeiss lens
"There are a great many things I am in doubt about at the moment, and I should consider myself favoured if you would kindly enlighten me. Signed, Doubtful, off to Canada." (BJP 1914).
Here's what the double line bokeh and donut shaped highlights look like from a Soligor compact 500mm/8.0 macro mirror lens (pay attention to the background)--
Too bad, because this was such a compact little lens to carry around, and the close focus ability was a plus. Contrast was also lower than a refractive lens, but in this image of a great egret in full sun, I could have used even less contrast.
Here's the smooth bokeh of a Canon FD 600/4.5 refractive lens--
Don't waste any money on cheap mirror lenses! They are optical not very good. A used rare (former East German) Carl Zeiss Jena 5,6/1000mm mirror lens in good condition is costing today approx. 3000 Euro's, without camera adapter. Advantage of this lens is, it works fine also on medium format cameras.
The inside element is a replaceable glass and comes clear, yellow, orange, red and polaroid.
I was puzzled by that but I assume you refer to an inserted filter and in the latter to a polarizing filter.
At times the manufacturers marketed those lenses because of those rings. I personnally got my problems sometimes with those doubled lines.
Anyway, this is a matter of taste and subject. By using a simple mask cut in shape as you like as additional aperture in front of the lens you can change the of out-of-focus image.