It most certainly does matter, but it's not a speed thing.
32 bit operating systems are limited in the amount of memory they can address. A 32 bit pointer can cover an address space of 4GB, and the OS further divides that up. You end up with a little over 3GB usable memory with a 32 bit OS. 3GB is not enough memory for modern applications and operating systems.
Using a 64 bit operating system removes this limitation, allowing you to get the standard 8GB of memory, which is plenty for 99% of people. More than that will not make your computer faster, contrary to popular belief. A decade ago more memory meant a faster computer, but we've long since left those days behind when there simply wasn't enough memory to hold all the running applications. Now, going from 8GB to 16GB just means you'll have another 8GB of memory that is doing absolutely nothing.