I much prefer Trollbeads. They came out in 1976 and have a selection of beads rooted in mythology, symbolism, and elements. Their glass beads are stellar.
In fact, Pandora glass is designed by one of Trollbead's designers and Pandora must pay a "royalty" fee for the special silver core used on the glass to Trollbead for the next 25 years. We won't call it stealing, but let's just say the owners of Pandora used to be closely associated with Trollbeads.
Pandora is more widely known because of their blitz style of advertising and trying to locate themselves in spots like jewelry stores and malls. Usually you will find Trollbeads in smaller boutique style shops, although they have opened several concept stores and kiosks in the past year.
Personally, I feel that Pandora is more "safe" in their beads...soccer ball, hearts, etc. whereas Trollbeads has trolls, fairies, scary faces, dark colors, etc. To be sure, they have their share of lovely flowers and romantic themed beads, but they are done in such clever ways!
I think if you want ease of finding beads and are a bit more mainstream, you might find Pandora the better choice.
If you want truly unique beads and don't mind having to go on a treasure hunt for them, go with Trollbeads.
I'm sure it is obvious that I have strong feelings! LOL....