The Beetle is only about $1000 more than a Golf for similar trim levels. Why would you spend it? First, it's a tad safer than the Golf. It's also lighter, and thus better on fuel by a slight amount. Of course, it's a unique looking car as well, but there are mechanical reasons to buy it.
As for Bug vs Mini, I'd go for the Bug. The Mini has the same base price, and currently it's a new model. Why is that important? the first 2-3 years of a new model is always the time during which the manufacturer works out the kinks. I guarantee you there will be at least small problems with the Mini, though perhaps not big ones. The Bug has already had all the wrinkles ironed out.
The Mini hasn't been put through tests yet, but it would be hard for it to top the Bug in terms of safety. That's a big plus in these small cars. I can personally attest to the fact the Bug is indeed safe, and it's comforting to know that when you share the road with two-ton SUVs.
If you want to talk engine, the Beetle is all over the Mini. Right now, the best engine available for the mini is a 160-hp supercharged version. The Bug now has a 180-hp 1.8t. Also, the 24-valve 201hp VR6 is coming to the US and may arrive in the Bug as well. I'm pretty sure the suspension and handling will be superior, but we'll have to see what the Mini is capable of first.
At this point, the VW has everything over the Mini, except the glitz of being the new kid on the block. However, we haven't really seen what the Mini is capable of, so I'd give it a couple years before I really compare them.