Saint Seiya is a well known classic, and one of the first anime/manga that anime lovers watch/read from their childhood..
Saint Seiya next dimension takes place mostly in the 18th century, the previous holy war between Athena and Hades, mixed up with the 20th century after Athena and her saints defeating Hades. But if u expect to see the same characters from lost canvas,, then your wrong.
Kurumada is the one in charge of everything here, so the characters including the gold saints are different from Lost canvas. there are a lot of betrayals among the saints, which we did not see so often in the other series of saint seiya, and the story is almost the same as the original sanctuary arc from the first saint seiya manga. like the pop trying to kill the baby Athena with the same knife, a gold saint saving her and being announced as a traitor...
but even though a lot of stuff look the same as the original, its a manga that any saint seiya fan would certainly enjoy.. the fights are amazing as always, a lot of new things are there, new god, witches, even Artemis and touma are present.
Even if you are new to saint seiya, you will still enjoy this manga. but don't read this expecting that the events from the previous holy war are the same as the ones from lost canvas.
i would just suggest you to stop reading reviews , go ahead and start reading it. you will not be disappointed. But i think you would understand this better if you read the original manga first.