Originally Posted by chips11
The new machine has an Intel Core 2 Duo (P7450) 2.13GHz 3MB (L2 Cache)
The older machine has an Intel core 2 duo T5600 1.83GHZ
Each of the T5600 and P7450 can run your choice of two architectures: IA-32 or X86_64. Neither can run IA-64.
IA-32 is the common 32 bit Linux architecture also known as X86 and often known by related architecture names, such a i686.
X86_64 is the common 64 bit Linux architecture also known as AMD64.
Linux supports many other architectures, several of which are 32 bit or 64 bit. But those two are so common now that if a distribution just gives you a two way choice of 32 bit or 64 bit, it means those two (IA-32 or X86_64).
Which of IA-32 or X86_64 would be better for you to choose is a complex question, and the answer isn't that important. They will do the same things, probably with only a slight difference in performance.