I never saw Happy Endings as Friends: The Next Generation, beyond being about a group of late-20/early 30-something people.
What more would be needed, though? Maybe if two of the characters were married, two in an on-again/off-again relationship, and two were just friends that were really close? Would that make the parallels closer?
In other words, 'if Happy Endings was more like Friends, it would be just like Friends', but it's not -- so it isn't.
From what I have seen, Friends is pretty much a Seinfeld clone, similar to the way "How I Met Your Mother" is a Seinfeld clone (and dozens more), with romance. "Endings" is a product of the post Seinfeld sitcom legacy too, just a somewhat different strain as has been pointed out. Call the two shows "cousins", not twins.