First, about that XP machine. The OS's job is to stay out of the way 99% of the time while programs sit there and run; a better OS doesn't make programs run faster, just does a better job of staying out of the way. So if Windows XP doesn't have the power to do something on your hardware, neither does UNIX. I made the same mistake a long time ago, trying to install a modern Linux distro on a Pentium (no II, III, IV, or D). 32 megs of RAM. It swapped like a wounded moth
Further, distro's advertised as "easy" are aimed at modern consumer PC specs and have grown-up resource requirements. Install that loadout on an
old computer(Anything with an XP sticker is likely 10-15 years old) and it will be sucking sand. Your best bet for that kind of distro is to install on a computer one or two models behind - old enough its hardware is well-supported, but not so old that its performance is poor.
What Linux is better at than Windows, I think -- even in the era of quad-core computers - is sharing processing power so things don't lag out as much. Linux couldn't do miracles with my ancient, dismal Duron, but it
could run a compile and an MP3 player at the same time without stuttering.
If you want a general purpose Windows like experience with a lot of default choices made for you, try Ubuntu. If you want to build a super lean task-specific machine, try Debian.