One thing I want to make clear: Tadrart Acasus and Tassili n'Ajjer, the eastern section also called Tadrart, are hardly distinguishable. If you visit the Algerian side you should only have a reason to visit Libya due to bordered defined by the UNESCO committee. The rock art is on both sides but I feel the countries don't want to cooperate and Algeria is limiting the site to what it is now, the western section of Tassili n'Ajjer NP. At the moment the Libyan land border is officially closed so you need to hike over the Tadrart plateau to get into Libya only to claim you have set foot into it, something I can't say is worth it. Or come from the Libyan side which involves a long, long drive and then the park may still be officially closed anyway.
Overall I find that both sides of the border are rather crappy for world heritage but get high ratings because the entire tour involves an adventure; trekking, camping, Touareg hospitaly, nomad camps, rock formations, sand dunes that keep going, magnificent sunsets and sunrises, and of course the whole remoteness. However, that should not really count for the site - that's just a vacation tagged on.
While I do rate the art higher than most I have seen ranging over a huge time period, and it's interesting to see different animals that no longer call it their environment such as elephants, it's just not the amazing part of the trip you do it for. One thing that you see more are test art, drawings that ended up as failures which you often find missing from sites and wonder how they only left the "good" art on the walls. Here you also find half finished drawings and overwritten, perhaps on purpose or by mistake.