High Tempo = quicker decision making/passing. As mentioned good for counter and direct play. However the quick passing and decisions often leads to turnovers, rushed shots, and excessive long shots if play breaks down.
Slow Tempo = Relaxed urgency offensively. Will not ALWAYS look to make risky passes and flick ons. Will pass the ball around and keep ball at feet for a little longer.
You just need to think of them in regards to getting into the final 3rd. Quick wants to get into final 3rd "quickly" and get shots off. Slow will get it into final 3rd but without bravado.
I use to play at a very high tempo, but I had to turn it back to normal because I realized that my players would get trapped about 20 yards out, and instead of backpassing, they would shoot and miss. By slowing it down, I gave my players the time to work their way out of their trap and I've actually noticed my players being more creative since they weren't rushed into shooting or passing.
Oh, btw I use direct passing and normal tempo, provides more throughballs. If you can balance your formation and player duties, quick + short passing and direct + slow passing is very much possible.