Polarizers do not have the haze cutting abilities that the red filter has. If you want to darken the sky but still have a sense of recession but allowing distant objects to be "hazy" then the polarizer will do the job better than the red filter. This would also apply if you were photographing mist but still wanted a darker sky. I understand that green filters (as opposed to yellow green) have similar properties.
I have both Red and other coloured filters together with a Polariser.
The effects are different.
As many of the previous posts have indicated you need to try them out to see how they affect your sort of photography.
The weather, atmospheric conditions and subject matter all have major influences on the effects you get – so unfortunately there is no one size fits all rule – you have to work it out for yourself.
If you are going to do more B&W work, then you might quickly find that only having a Red coloured filter is rather limiting – Red can be a very harsh, and you might need a range of filter colours to give more subtle effects.
Personally, I only shoot B&W and have over the years built up a range of 7 different coloured filters plus a Polariser for each of the filter sizes I have.
90% of my work can be covered with a medium yellow, a medium orange and a yellow/green filter.
Of all the Filters I own the Red filter and the Polariser are the least used – but it’s a very personal choice – YMMV
I too do not use the red and polarizer filters much.
The polarizer dulls things terribly, and is of very limited use.
The red filter is not a correction filter, but well and truly an effect filter, and the effect is not very often called for.
Shoot a couple of frames with the polarizer and compare to your older B&W shots with the red filter. Try to find the same or similar scenes for a more reliable comparison. This will give you an idea of the relative effects of red vs. polarizing filter.
As some have said, the red filter will change the values and relationships of the lightwaves reflecting off the objects in your scene. This means that blues and greens will be darker than they appear to the naked eye, and reds and oranges will be lighter than they appear to the naked eye.
A polarizer does something different entirely. It changes the angles of reflections of lightwaves if used at appropriate angles to the sun. This reduces light reflection off water, darkens blue skys, results in more saturated and vibrant colors.
So, like I said, shoot some frames with the polarizer and b&w film and you can decide for yourself which look you like. You can combine them as well.
I have found that with a 35mm camera on a bright day and ISO 400 film a red filter plus polariser still give speeds that are handholdable. It is a dramatic effect and in the right scene well worthwhile doing. If you want to use a tripod then fine but if you don't normally carry one then check the shutter speeds obtainable with both filters. I'd be surprised if you cannot handhold at said shutter speeds.
Depending on your latitude, lens and desired aperture and of course light conditions, you might manage handholding at ISO100 withn the combo of red plus polariser.
You should use the filter or filters that give you the effect you want for a given picture. Red filters and polarizing filters do totally different things. Polarizers change the direction of light rays entering the lens, and colored filters *effectively* (not *actually*) change the spectral sensitivity of your film.
For 95% of pix, I don't use filters. If I had to make some sort of blanket rule for myself, based on this examination of what I do naturally, it would be to use NO filters. However, who needs to make arbitrary blanket rules? I use filters every now and then, depending on the picture. Usually yellow, yellow-green, or orange. Sometimes blue or red (and very very very rarely will I use red if there is a blue sky in the composition). I have even used a polarizer a handful of times, though they frustrate me trying to figure out where to set the darned thing. I hate having to fiddle when trying to catch a certain light.
As for the "red should not be used for color" statement...well, yes, it should be, if you want your entire picture to be tinted red!