Neither are actually immortal.
Also it's a Rinnegan.
did he said that he can achieved Immortality From Rinnegan:wut:
In one of the last chapters when he's fighting Naruto. There is a panel in which he says. That he achieved immortality and can take the hatred on himself to eternity or something.
Because Sasuke isn't immortal, and neither is anyone else.
1 - He has Rinnesharingan (Rinnegan + Sharingan).
2 - Hagoromo died because he extracted the Juubi and it blocked his Rinnegan powers of Immortality (As what happened with Madara) or Hagoromo ran out of power.
The only person to die of old age who awakened the rinnegan is old Madara but Kishimoto could say that old Madara died since he gave his rinnegan to Nagato.
It wouldn't be a surprise to me if rinnegan granted immortality considering it can bring people back to life and has many hax jutsu.
There's no solid evidence to say it grants immortality but kishomoto can do anything in his manga, he said in a interview that orochimaru is basically immortal so he could make Sasuke immortal due to rinnegan power so Sasuke can keep a eye on Orochimaru.
If Rinnegan made you immortal then there was no reason for Hagoromo to die.
Mangafax says Hagoromo was going to die even with the Juubi and Rinnegan. He split the Juubi and sealed it in the moon before he would have died.
The biju are, so is hidan lol
I think Hogoromo died due to getting the tailed beasts extracted so if Kishimoto wanted he could say Hogoromo was immortal, anything can happen in manga.
It could be that Hogoromo wasn't immortal but even then getting the the tailed beasts extracted will kill you unless you get them put back in.
1 - He has Rinnesharingan (Rinnegan + Sharingan).
2 - Hagoromo died because he extracted the Juubi and it blocked his Rinnegan powers of Immortality (As what happened with Madara) or Hagoromo ran out of power.
Because Sasuke isn't immortal, and neither is anyone else.