I have both types each with 2.4 P4 and 512k RAM. PC Mark 2002 gives the following results:-
Desktop cpu 5703, memory 5429, hdd 902.
Laptop cpu 2662(5736), memory 2463(4464), hdd 395(365)
Figures in bkts are with mains charger connected and the desktops hdd is a fast one so I guess it depends on what you use it for. Hdd speed is likely to be your biggest difference in use (they are the right way round so I don`t know why its slower with the mains!).
Graphics on the laptop are provided by a Mobility Radeon with 32mb RAM. On 3d mark 2001se it scores about the same as an older PIII system I have with the same RAM but is much lower than the desktops fancy new card!
Workwise, I do nearly everything on the laptop and backup to the desktop but other than Solitare I don`t play games on it! The desktop is much better for that!