I am running Logos on top different desktops and desktop with the slower CPU (AMD X2 5000 vs. AMD X2 5400) is noticably more responsive. Although it has a slower CPU it has more RAM (4 MB vs. 3MB) and its intergrated video card is much better (ATI HD3200 vs. Nvidia 6000 something). What I really nice it when I right click the popup box is populated much faster in the system with more memory and better video.
The interesting thing about the system with the HD3200 graphics is that if you put in a ATI HD3450 or 3470 it essentally becomes a duel graphics card system and almost doubles in video preformance. I found such a card at NewEgg for only $35. With the greater graphic processing power and with 512 MB video memory, this will be a cheap way of increasing Logos 4's preformance.