More to the point, throwing away one of something every year or ten is more environmentally friendly than throwing away seven of something every month. Provided the one thing you're throwing away isn't horrifically environmentally destructive.
The tampons still have to be manufactured, individually wrapped and packaged, and delivered to the customer. Let’s say a single menstrual cup lasts five years and a woman has periods for 40 years. That’s 8 menstrual cups and a HUGE heap of tampons. I’d vote for the cup.
zoul makes my point better than I did... the distribution and packaging costs and effects are definitely important. I also have a bit of unfounded reservation about assuming something that's touted as having been designed to be biodegradable actually is completely and totally so... it just does not seem likely to me.