I was aware of Diva Cups (though I've never tried one) but I had never heard of Glad Rags or Party in My Pants. I'll have to research those.
Diva Cups are very popular with backpacking women, who don't want to deal with carrying a ton of tampons into the backcountry and having to carry the used ones out. Fortunately, my backpacking trips haven't landed at that time of the month thus far.

I have fibroids and have very, very, VERY heavy flow for the first 2-3 days...I have my doubts whether a cup could handle that. I've been given meds to help stem the flow a little and sometimes it helps and sometimes it doesn't. This has been going on for over 10 years and it does seem to be improving as I get closer to menopause. I'm almost 49.