The best counters in a PIC are the integral Timers, even better if you have CCP (Capture Compare) Modules in the PICs hardware.

If you're trying to count uS in software then you have to take into account the software latency in achieving the count. 1uS will be tight to achieve... apart from the fact that in PICBasic you don't really know how long any given instruction will take to execute. In Assembler you have a better chance since each instruction (example NOP) is only one or two clock cycles (see Assembler instruction list at the back of any PIC Datasheet).

Finally, remember that 1uS will not be 1.000000000uS when relying on the PICs crystal because they're seldom that accurate... they vary with temperature, voltage, windspeed and direction, beer, garlic...