From the official information for the Omega update:

The classic Atlas Path mission has been given a new breath of life, culminating in a final, consequential, choice. Witness the Atlas in all its grandeur, and decide whether to embrace the path it offers – or deny it. Either path will permanently impact your relationship with the Atlas.

But it turns out the "consequential choice" is the same one we already had, to birth a new star or not. The only difference is, from the same information page:

Players who decline the Atlas at the end of the Atlas Path are now awarded their own counterpart title and technology to those awarded for accepting its request.

Yay! A different title and technology. How that impacts your relationship with the Atlas, I have no clue. It's not like I have any ongoing relationship with the Atlas, after having completed both the Artemis and Atlas paths.

The conclusion to the Atlas Path has been visually enhanced and reworked, to create a more spectacular finale.

I didn't notice anything at all spectacular. There are some small differences, but nothing remarkable.

Choosing to birth a star or not marks the end of the path, now. The whole "go through a black hole to make the Atlas path go away" thing has been removed, which means that the Atlas path's annoying habit of popping back up again until you go through another black hole has been fixed.

Well, not exactly fixed, but replaced by a new permanent mission in which you can present wonders to the Atlas:

Players who have completed the Atlas Path now have access to a repeating mission with which they can earn nanites and additional words in the Atlas language.

Those additional Atlas words aren't worth anything if you've already completed the Artemis path. It used to be that you could review the log of the Atlas path, and the translated words of the Atlas would be filled in as you learned them. Learn the whole language, and you could understand everything that the Atlas had been telling you. Well, all except one word. The log of the Atlas path has been removed, so you can no longer review it.