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.