My general opinion on the points/dice quandary is that it depends on how gamist the group is. By that, I mean how much the game is designed to test the players, rather than the characters, and I mean that in a very broad sense. The main reason is that I want to see both edges of the sword sharp; if you've got the potential for rolling all 18s, you shouldn't expect to be shielded (much) from getting all 3s. If it's just a matter of wanting to be better than what's possible with point buy, the group should discuss handing out more points (per 3E). Having a below average character can be fun, but significantly increases the odds of getting dead, which really messes up a narrative, thus should be reserved for groups that look at it as more of a strategy game than cooperative story telling (caveats apply).
While I'm willing to play at a gamist table, my group tends to be more of a casual approach to a heroic tale, with enough dice to add some spice (which is my preference, too). A point here or there isn't a big deal, but too much swing between PCs tends to remove the heroic aspect from some of them -- even when it's average vs. above average. When we picked up 5E, I left it up to the players; two used points and two rolled. Of those that rolled, the other had (after racial mods) an 18, two 16s, and nothing under 10. It quickly became his show, with the other PCs as supporting cast, not because he was a better player, but because he didn't have much need to rely on anyone else, other than as meat shields. Since we were explicitly in a test mode, we eventually had him level off the character to a point buy and things went to even footing.
Like I said, it's a style thing. Neither way is "wrong", but each facilitates different play experiences. If I was going through Tomb of Horrors or Rappan Athuk, I'd absolutely be up for random scores and ability score minimums for various classes/races. Good times. Doing Dragonlance, Ravenloft (I6), or even Age Of Worms, not so much.
