Windows XP Professional Edition provides a strict superset of features, capabilities and functionality found in Windows XP Home Edition. As such, there is no real performance difference between the two versions, at least, not in a way that would affect the performance of any decent system.
The best way to describe the differences between the two versions is to list what Home Edition is missing.
Windows XP Home Edition lacks the following features in comparison with the Professional Edition:
Remote Access Desktop
Offline Files and folders
SMP, or Multi-Processor Support
Encrypting File System (EFS) for NTFS
Access controls for files, folders, applications and other resources (NTFS Security features)
Dynamic Disk Support
Software Installation and Maintenance (automatic software installation, configuration, updates and removal)
Internet Information Server and Personal Web Server
Roaming User Profiles and Multiple Roaming
Remote Installation Services and the entire IntelliMirror management services technologies
Multi-Language User Interface
Sysprep (System Preparation Utility) support
Domain Membership on networks
IPSec User Interface
Simple TCP/IP services
Client Service for Novell Netware
In addition, the following features, although available on the CDROM, are not installed by default:
Automated System Recovery
If you feel that you can do without any of the features listed above, you should consider Windows XP Home Edition. If you do need the above features, then you should select Windows XP Professional.