The binary RPMs are usually compiled for a specific CPU to gain increased performance by taking advantage of new architecture and instruction sets. Every new generation of CPU has some new features besides just increased clocks.
i386 - is the old 386/486 CPUS
1586 - is original Pentium/Pentium Pro
1686 - is the Pentium II/III
As a general rule, use the one for your CPU. Older versions will run on newer CPUs but newer ones might not run on older CPUs.