Rotated a Pi 3 B+ out of my "production" and put in a Pi 4 so I had this one for toying with. Downloaded the 64 bit OS, flashed and installed it. This is completely without any "scientific" methodology but the install felt faster. The boot up seemed quicker and the install seemed to be about half the time. Setup all the normal parameters, name, wireless IP, screen etc then rebooted. Opened a prompt to look for updates and it said no communication. Apparently it couldn't find my router. During setup it saw my wireless took the IP and name and password and kept going. Still when I tried to surf or otherwise get to the internet no go. Pounded on the box for about an hour then reflashed the SD with 32 bit and drove on. No, didn't try ethernet because the switch is on the other side of the room and there isn't a bench and I really wasn't looking for a long term experiment and I didn't have a really long cable. But, for a test OS it seems like it has a lot going for it in terms of speed advantage.
In case anyone is interested.
I highly doubt that you can see any performance difference between the 32bit and 64bit version in normal operation, the main reason for 64bit is to address more than 4GB memory, ie. the 8GB version of the Pi. Only if programs move large chunks of data and the programs are taking advantage of it, you may see a difference due to the memory pointers. It is more likely that you see a difference because of the clean install 
The 8GB of the new Pi4 are even usable with the 32bit Raspbian, but limited to 3GB per process. That is made possible by the Kernel's Large Physical Address Extensions (LPAE).
I doubt the older Pi3 will benefit from a 64bit OS due to the limited RAM size of those models. All pointers are 64bit and require more memory.
As I pointed out , totally unsupported times, just a feeling and as pointed out by others probably not accurate. I suspect it felt faster because I wanted it to be better.
Also remember that the boot speed will be affected by the speed of the SD card, so changing to a different card type can make a difference.
Well the pi 3+ runs at 1400Mhz while the Pi 4 runs at 1500Mhz so it is a little faster...
err - this is still on a Pi3+ - same hardware, different OS.
err - looks like he's talking about the Pi4
I think that is the key phrase, 'this one' refers to the original 3.
Ahhhhh...light dawns on marble head 
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