BBB I/O capabilities? (Pulse counting)

I’m trying to figure out which of the various tiny systems (BeagleBoard Black, Raspberry Pi, etc…) to use for a project.
One thing I will need to do is pulse counting on a bunch of input lines.
These will vary from 1K/sec to 10K/sec.
I need to figure out if I can make pulses cause interrupts (preferably interrupt if any of a group of 8/16/32 changes state), and have a simple counting interrupt handler.
There would also be a set of output pins that would be PWM’d at some stupidly low rate like 10Hz. (Just as many of these as input lines.)
The only other things the program would be doing is sending the counts off to a server once/second, and occaisionally receiving commands to change the various output PWM duty cycles.

How many I/O could I do with a BBB? Can I have 32 input pins cause an interrupt if any one (or more) of them toggle state?

If you don't need loads of raw processing power or the advantages of Linux I would look for at the audrino family. These will be a lot easier to accomplish the type of tasks you are attempting.