The A31p is a discontinued, 2+ year old model. A good machine, ask Bill (he runs this site and he owned one, I believe), but here's what you're looking at:
A31p is HEAVY - 7.7 pounds v. T40 5 pounds or so (not sure what the kg equivalents are)
A31p uses an older, power-hungry mobile Pentium 4 (2 hours battery power if lucky, v. 4+ hours with T40), slower RAM, slower CD-RW, slower hard-drive, very old graphics chip which doesn't even support DirectX 8 in hardware... I could go on.
Depending on which model of T40 you're interested in, the T40 probably outclasses the A31p in every respect except for the 15" UXGA Flexview screen. However, I wouldn't give up all the benefits of the T40 just to enjoy the screen of the A31p.
I'm sure there can always be a case made for the A31p in terms of price/performance/features. But laptops tend to age quicker than desktop computers. And the A31p is a bit old if you intend on tackling the latest/greatest software/games, etc.
Hope this helps.