Re: being a remake of ANH: having seen it a second time, I think the movie really stands on its own starting with the lightsaber battle in the snow. Up to then, it's certainly entertaining and enjoyable, but the plot does tread very closely to IV. But once Kylo, Finn and Rey start duking it out, you're immediately invested - it's just such a great fight, particularly with the fist-pumping moment of Rey snatching the lightsaber. It's also where the movie parts ways from IV, and it's certainly better for it.
That said, the characterizations of each of the characters - Finn (Han/Luke), Rey (Luke), Poe (Han/Leia), Kylo (Vader), BB-8 (R2-D2) - are different enough from their OT analogues that the movie still stands on its own terms. However, Hux is pretty much just a blatant ripoff of Tarkin, though with a more North Korea ish edge, rather than Nazi ish.
And that's another thing - Death Star III feels different because previously, the Death Stars were ultimate weapons of the nation already in power. Basically just icing on top of their authoritarian cake. More symbol than anything else, though still effective militarily. But Starkiller Base feels more like if North Korea gets a nuke and starts bombing other nations. No one's expecting it - it makes the dynamic between the players different.