I think this judgment is popular as Raspberry Pi 3 model B and Beagle Bone Black are the most popular versions produced, and the comparisons are held extensively between these two, but there are other models and versions that could change your point of view as will be mentioned later.
In this regard, we can say that Raspberry Pi 3 ( RPI3 ) is better than Beagle Bone Black (BBB) for the following reasons
The connectivity, RPI has more solutions for communication like Bluetooth and WIFI which are built in, in contrary to BBB which can accept external hardware (more money and more space needed) but at the expense of the USB port
RPI has 4 built-in USB ports which make it capable of supporting mouse, keyboard, flash memory and so on at the same time, on contrary, BBB has only one. Of course, you can extend its ports using USB hub but it has disadvantages with current consumption and space occupation especially if your project is confined
HDMI and USB Cables, RPI supports Full HDMI cable (the popular one ) while BBB supports the Micro one which adds an extra headache of getting out an adapter to adapt the normal cable chord with the HDMI slot.
Also, BBB does not use the micro USB for powering up like RPI but the mini.
The processor speed and RAM size, RPI runs with quad cores at 1.2 GHz each and 1 GB RAM While BBB runs with a single core at 1 GHz and 512 MB RAM.
One of the most advantages of RPI3 over BBB is the storage capacity, RPI has an external SD card in which you can upgrade its capacity as you need while BBB has a built-in memory limited to 4 GB, this can make great limitations on the applications you are working with especially if it needs high memory capacity.
Beagle Bone Black has an advantage that is not offered in RPI which is supporting reading analog inputs like Arduino.
But you could change your point of view when you see the Beagle Bone Blue for example, which is oriented for robotics applications and Beagle Bone Black Wireless that extended the black with built-in wireless and Bluetooth modules, however, both of them still have one USB port and built-in memory.