What is the difference between hardware and software breakpoints?

Hardware breakpoints are actually comparators, comparing the current PC with the address in the comparator (when enabled). Hardware breakpoints are the best solution when setting breakpoints. Typically set via the debug probe (using JTAG, SWD, ...). The downside of hardware breakpoints: They are limited. CPUs have only a limited number of hardware breakpoints (comparators). The number of available hardware breakpoints depends on the CPU. ARM 7/9 cores have 2, modern ARM devices (Cortex-M 0,3,4) between 2 and 6, x86 usually 4.

Software breakpoints are in fact set by replacing the instruction to be breakpointed with a breakpoint instruction. The breakpoint instruction is present in most CPUs, and usually as short as the shortest instruction, so only one byte on x86 (0xcc, INT 3). On Cortex-M CPUs, instructions are 2 or 4 bytes, so the breakpoint instruction is a 2 byte instruction.

Software breakpoints can easily be set if the program is located in RAM (such as on a PC). A lot of embedded systems have the program located in flash memory. Here it is not so easy to exchange the instruction, as the flash needs to be reprogrammed, so hardware breakpoints are used primarily. Most debug probes support only hardware breakpoints if the program is located in flash memory. However, some (such as SEGGER's J-Link) allow reprogramming the flash memory with breakpoint instruction and aso allow an unlimited number of (software) breakpoints even when debugging a program located in flash.

More info about software breakpoints in flash memory

This article provides a good discussion of pros and cons: http://www.nynaeve.net/?p=80

To answer your question directly software breakpoints are more flexible because hardware breakpoints are limited in some functionality and highly architecture-dependant. One example given in the article is that x86 hardware has a limit of 4 hardware breakpoints.

Hardware breakpoints are faster because they have dedicated registers and less overhead than software breakpoints.