You don't give full details of the specs of the laptop and desktop, but there are other factors.
1] Processor speed and performance
2] Disk speed, 2.5" versus 3.5"
3] Graphic card performance. More often than not a laptop has it's video card integrated with the motherboard and shares RAM. On the other hand, desktops can have dedicated graphic cards with their own memory.
4] Running processes, and viruses and other malware.
That Intel Pentium III seems an old type now. dating back to 1999. How old are these two computers?
My laptop has 200 MHz and 384 MB more RAM than my desktop. Same type of RAM and Processor (PC133 and Intel Pentium 3), but my desktop is faster. How come?