For many many years my group used to use the 4d6 six times ignore the lowest dice method.
However players invariably proved unreliable and had to be watched like a hawk to prevent cheating (not the malaicious sort, but the I don't want to play a poor character kind). Inevitably we used to end up with every character having "supposedly" rolled on 18 and two 16's etc... and I as a GM totally hated that method, noone wanting to play the average character....
So I switched to the basic 3d6 method rolled six times and you get what you get and thats it beyond racial modifiers... and this provided to be far more reliable, though the players griped and groaned about thier characters being rubbish....
Also with both the above methods you also can have characters that can vary hugely.... and random rolls can totally ruin concept, i.e you want to play a ranger what if you don't get any stats at levels that work with that ideal... in second ed you also had stat requirements to enter a class...and with random rolls that used to be a problem too....
When 3e came out I approached the points buy method with reluctance...however my opinion changed completely when I used it. why, well simply put every character is on an even par.. they have the ultimate control on which stat is what upto the points limit given, it makes life easier for the GM, and provides the players what they want.
This is not however to say the points buy method cannot be abused.. I can't even begin to count the number of GM's who use the 40 or 45 point allotment per character and totally fool themselves into thinking they are playing a balanced campaign.... as it isn't, not even close its a high powered campaign and then some. Me 25 points I preferred, though I did allow my group to talk me up to 28 points but thats all they get and that works fine, the balance is right, the characters are right...and all is well in the world

)
Note to self..must breath more
Gaaaaaaaaaaaaaaaaaaaaaaaaaassssssssssssssp!
Ah thats better