I use divacup as well.
You can probably feel it if you think about it, but it's not much different than tampons in that sense. It's certainly not uncomfortable if you put it in right. (they are a little tricky to get in right at first but you get used to it)
As far as health goes, I think it's less likely to give you TSS or infections because there's not cotton up there collecting bacteria and such, and drying and irritating your vagina. I've found that the cup leaves my vagina feeling much happier than tampons did. I have never had a problem with infections. Read what mylove4u said, she explained it.
Divacup can't be worn during sex, but that's not a biggie, just take it out and then have sex! And I really liked that I only have one that lasts me a long time, so I agree that the disposable ones seem a little counter intuitive. I love that I can just clean it out and I'm good to go. I don't have to spend money on tampons every month, and I don't have to carry extras around with me, and I'm not polluting the environment with my menstrual needs! Divacup is available in canada and I love it.