D&D 5E (2014) Is Point Buy Balanced?

It's more balanced than rolling attributes, less than using Standard Array.

In the end, it comes down to personal preference and the kind of game you want. I've seen one game where the PCs started with all 18's, and one 19. That was some time back in 3E, BTW.
Lack of OP reading is strong with you.
 

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I once was told characters need at least a 14 in constitution alone to be effective.

IMO Constitution is the most overrated ability but players tend to want it over others in general and the talking heads online with the optimizer builds always stress it. On most players I've seen other than me it is typically the 2nd highest or 3rd highest stat.

For me on point buy it is usually a 10, sometimes a 12. It is a 14 if I am playing a subclass or species that uses it.'

To answer your specific question though - no the combinations available with point buy are not all equivalent.
 

Rolling stats is on average 31,3 pts.
point buy is 27pts
standard array is 27pts.
so yes, pointbuy is underpowered.

in general, I prefer increased point buy with not ASIs from race, background or feats.
or standard array that is increased, depending on power level you want to have in game.

IE:
20,20,16,14,12,12
20,18,16,14,12,10
18,16,14,12,12,10
16,14,12,12,10,8
14,14,14,12,12,12,
14,14,12,10,10,8
 

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