Not talking about using your browser to connect to sites. I'm talking about your LW connecting to the gnutella network. The network has nothing whatsoever to do with connecting to sites, you are connecting to other users.

LW Pro connects to 5 ultrapeers instead of Basic's 3, thus should improve in searching for rarer files by reaching a wider audience of file sharers.
LW Pro has the ability to download from up to 10 hosts per file compared to Basic's 8 hosts per file, thus should in theory result in faster downloads.