The short and somewhat oversimplified answer to "What is the performance of a Linux install like?" compared to XP is "slightly better than XP on the same hardware." That does depend on two factors, however - how clean your XP install was and what flavor of Linux you choose.
By this point, a PC running an original XP install is very likely going to be bogged down by a combination of bundled software and a combination of antivirus and anti-malware tools taking up valuable memory and CPU time looking out for threats - or even some of the more insidious types of malware themselves.
Installing something like Ubuntu 14 on an older machine might not be quite the boost you are looking for due to memory requirements but one of Linux's strengths is the many variations on offer.
Something like Lubuntu or Linux Mint LXDE can give you the stability and software repositories of full Ubuntu but with a much smaller footprint.
