I have 32bit Ubuntu on AMD 64 machine, if I install 64 bit GNU/Linux will it will run faster?
It depends. On average it will use slightly more memory (possibly slowing it down) but also gain access to a lot more registers in the CPU. The difference is usually quite small.
It all depends on the programs that you run. If they are optimized to utilize the power of 64 bit computing then you will definitely find boost in performance.
Think of it like a vehicle... a truck carrying 32 tons of stuff can travel just as fast as a truck carrying 64 tons of stuff... this would be the frequency of the system... but their PAYLOAD is different.
The 64bit system can move twice as much data per 'clock tick' than the 32bit system... both may run at 2GHz, but the 64bit can potentially carry twice as much.
Here's the caveat emptor bit:
If the hardware allows it.
Think back to the old days (dinosaurs and stuff...).
There used to be 32bit processors being used on 16bit busses.... so while the processor could wail away on the data, getting it to and from the memory and devices was no faster than the 16bit systems, due to the bottlenecking at the data-buses.
Today's 32bit/64bit systems rarely encounter this any more... but keep in mind that your bus options now include the AGP,PCI,PCI-e, and whatever clever new acronym they're using today. "Speed" depends on many things, mainly how fast your devices can communicate with each other in the case.
For the most part... perceptually.... no, I've not noticed any massive increase in my systems going from 32 to 64bits. But the 64bit systems can access more ram, programs can keep more data in memory (max 2GB for a 32bit process, some whopping huge number for 64bit...(can't remember!))
You might, as a test, install the SAME distro in the 32bit version for a while... then re-install everything as 64bit... nothing really changes from a user's point of view. (From a programmer's POV... OMG!! Chaos! Ruination! nah.. it's neat!)