Both methods are intended to produce the same results as far as the bacteria are concerned. However, in theory, higher temperatures do more damage to the milk; in theory, longer times do more damage to the milk. That might make it seem like a wash between the methods -- damage it with heat or damage it with time -- but for a home-pasteurizer, trying to do 161° for 15 seconds will almost certainly involve heat AND time -- unless you have special equipment, you can't flash-heat the milk to 161° and immediately cool it down; you will heat it up over a relatively long time to reach 161°, and take some time to get it cooled back down.
Thus, most home users will go the low-temperature pasteurization (LTP) route ... OR they will skip pasteurization altogether. If you trust your milk source and how it has been handled in getting to you, you may want to use the milk raw, especially for cheeses that age 60+ days. If, like me, your only access to raw milk involves trucking in from another state, passing through several hands, and finally arriving in who-knows-what condition, you may want to LTP.