timer input capture for really low frequencies
It depends on the MCU and the timer clock frequency (APB in most cases).

Standard timers have 16 bit counters and 16 bit prescalers. They can measure up to 232 cycles, but the resolution would be 16 bits only. About 51 seconds at 84 MHz APB clock.

Some timers have 32 bit counters and 16 bit prescalers. They can measure up to 232 cycles without using the prescaler, in full 32 bit resolution, and up to 248 cycles with prescaling. About 38 days at 84 MHz.

Timers can be connected in a master-slave configuration, the overflow of one timer advancing the other. Combining two 32-bit timers would yield 264 cycles without prescalers, 296 cycles with prescalers. About 3*1013 years, more than 2000 times the age of the universe. And more than 2 timers can be connected that way if that wouldn't be enough.


  I just use a standard interrupt and use the system clock to get my period measurements? Is there even a difference in the two approaches?


Interrupts can be blocked by other interrupts or code disabling the interrupts. The counter is read by interrupt code that needs some time to execute, causing imprecise measurements. A timer stores the capture value at the exact cycle when the trigger occurs.