Well, other than the already stated Astral vs. Umbral differences, their origin is also inverted.

Voidsent were created by the Ascians' plans succeeding all too well. When the Flood of Darkness happened, it was intentionally done without the knowledge that flooding the shard wouldn't rejoin it. Only in the aftermath did they discover that this was not the way to go.

Sin Eaters were created when Ardbert half killed a fused Ascian with the Blade of Light. This ruptured the delicate balance the Ascians had brought about, cascading into a Flood of Light that was stopped by Minfilia. This rendered the First salvageable for a Rejoining, and so the other Ascians, namely Emet-selch, took measures to control the Sin Eaters. There was the creation of Vauthry, but if you notice when we defeat Mitron in Eden, there was no need to soak up his soul, and his soul did not have the same properties as all of the Sin Eater Light Wardens.

It's never explicitly stated to my knowledge, but this implies that the Light Wardens were crafted by the Ascians. Designer monsters, so to speak. Which we know now from Amaurot and Elpis was their specialty.

It could be that Sin Eaters would have developed a more tranquil form of the Voidsent culture we see now in the 13th, if they were left alone or if the Flood hadn't been stopped. They weren't though.

Not too mention, the Lifestream for the 1st is intact, unlike the 13th. Meaning that Sin Eaters still have the flesh and soul dichotomy going on, whereas Voidsent barely do, sort of.