I would use both if I had a choice, but my stock "Melzi" board doesn't have enough inputs as near as I can tell. Most of the (scarce) instructions show to disconnect the Z switch and connect the BL Touch to the digital inputs in place of the switch.
I don't see any other connectors to wire up the EZ Touch to. Maybe the ICSP programmer, but I haven't messed around to see if that would be usable (nothing in the stock CR10 box is connected to it anyway).
So I think it's more of a practical issue that you use one in place of instead of adding.
However, less pedantically, why is a BL Touch better than a limit switch?
Two words: Auto Leveling
If you get everything setup right, auto-leveling should be great. I say "Should be" as I still don't quite have the board setup right. It keeps trying to push my nozzle into the PEI sheet, so I really DO wish I had both limit switches and the BL Touch.
Leveling on a hobbyist level 3D printer isn't that hard, but it's time consuming and requires some care. Having to do it every time becomes a colossal pain. So the idea that you could clean off the build plate, hit a button, and have the printer figure out what level was and just start printing is great. Not having prints peel off the plate because you had the gap set wrong, or didn't get the back corner leveled off, or the PEI sheet getting damaged because the nozzle ran into the sheet ... priceless.
But hey, if you're using a 3D printer where you'd even think about a BL Touch, you're on the DIY/Maker side, not the "stick in an SD card and hit print" side, so you should be used to figuring out how to wire one in. It's part of the adventure, right?