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.
64 bit is better. There are people who still need to use 32 bit to support legacy hardware that don't have 64 bit drivers. There was a big stink about this when Vista launched because people were pissed that their ten year old printers had been abandoned by the manufacturers and didn't have 64 bit drivers, so they blamed Microsoft. That colored a lot of peoples' perceptions about 64 bit operating systems, and there's still a lot of people around who think support for 64 bit is bad. It's not, it hasn't been for years.
As far as I'm concerned, there is no compelling reason for the average user to have a 32 bit operating system.