I don't use either. I try to be a little more umm... legal by paying $30. But I've never seen Limewire, my friend has BearShare, so I'll say Bearshare.
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If your paying money for a p2p client your getting royaly ripped off. Not only do the majority of p2p apps connect to one of a few major networks, but that money does not in any way impact the fact that downloading copyrighted material can result in lawsuits in excess of $25,000. All your doing is paying for a client that may be worse than some of the free ones, and for access to a network full of virii and spyware.
to the OP, i would advise you against using either of those or any other filesharing program. while a very small few like BitTorrent have legitimate uses, most are used almost exclusively for the spreading of files, music, and other copyrighted materials. The RIAA is suing thousands upon thousands of people, and do you want to try and explain to your parents why they owe the RIAA several thousand dollars?