The most notable difference is found with the wings, though it may be noted that a quick internet search shows there was some awareness of this change already. The Earthrise release, seen below on the left, features painted plastic wings whereas the Legacy Evolution release, on the right, is molded as tan plastic. This creates a matte versus gloss finish difference that immediately jumps out when putting the two toys side-by-side.
The "knee" paint is also noticeably different in the newer release. Earthrise Dirge features very purple knees (or perhaps kneepads if you prefer), as seen on the left once again in the image below. Meanwhile, the Legacy Evolution version sports a much redder shade of paint, landing somewhere between purple and lilac.
And those two small changes are really it, at least as far as this Transformers toy collector can tell. For most collectors these are not practical differences and add no reason to keep two extremely similar Dirge toys on the shelf, but it's always fun to see some variation when the same toy gets released years after its first outing.