In nearly all cases, modern computers will let you use slower clock speed rated RAM so long as it's physically and electrically compatible. The computer will just reduce the access speed to match the value as defined in the module's SPD.
The effective synthetic benchmark difference showed a little over 10% between 1333MHz and 1600MHz when I last experimented with it. The actual theoretical value is 25.6GB/sec for dual channel DDR at 1600MHz, vs 21.3GB/s for dual channel DDR at 1333MHz.
What that translates into in the real world will vary depending on what you're doing. Most of the time it'll probably be somewhere between 1% and 3% outside of situations where you're specifically bottlenecked by RAM speed - for example, really old games running at high display resolutions on an IGP. Having a larger physical RAM pool would completely negate the bandwidth issue and then some if you're running into swapping though.