After using Napster for the past few months, I just installed and began using LimeWire. Would installing BearShare give me access to more files, or are LimeWire and BearShare just two different programs that do the same thing and allow access to the same files?

they connect to the same network...so technically they should give you access to the same # of files... however the default settings for the respective clients are different so you may notice consistent differences between the two clients... bottom line if you want to see more files 1) increase the amount of hosts you connect to and 2) increase your TTL.