I have been pleased with Chanel makeup before. Chanel does not have a makeup counter anywhere near me though, and that's honestly a bummer because I have to order anything that I want from there, makeup-wise. In my opinion, Dior makeup has been really superb quality for me. It is pricey for makeup, but I have been really happy with multiple things from them.
I'm trying out their makeup brushes, and the quality is excellent. The bristles are very soft, and luxurious feeling. (It's pricey, the brush set that I got from them was 155.00 USD, but it will probably last for many years.) Very high quality. Also, I tried a trial size of Dior lipstick (for some reason, it's hard to get my hands on the trail size. Most often, only the full size is for sale.), and fell in love. It stays on me a long time, and it is very hydrating without being overly creamy, if that makes sense. (I love Charlotte Tilbury lip products, but sometimes I find that CT lip products are a bit overly creamy.). Dior eye shadow is also highly pigmented, in pretty colors. So far, I am trying out Dior makeup remover and I am satisfied with that--I'm satisfied enough to buy it again, but I do think with makeup remover that Neutrogena liquid makeup remover from the drugstore isn't a super ton different than liquid makeup remover from high end brands. I bought Dior backstage face & body foundation for the summer but haven't tried it out yet. Supposedly, it stays on through water, or at the beach, and supposedly, it is sweat proof. My fiance and I are taking our son to the water park this summer and I will be needing something like this. Although I purchased it, I have not actually tried it yet, but if you go on YouTube, Jeffree Star did a review of it and he was really happy with it. I think if I remember correctly, that he went in the pool and it stayed on or something but it's not a heavy feeling foundation.
I just want to add that my experience has been that all Dior makeup ordered from their official website comes nicely packaged in a Dior gift box (they're also doing free shipping right now, I think), with a pretty Dior ribbon and most often when you spend a certain amount, you get free samples and free trial sizes of their products. I've been satisfied with the packaging. I was happy that they didn't skimp on packaging.
So overall, I would say that if you are looking for makeup with a bit more luxurious quality that both of those brands are worth it. Chanel makeup I have been pleased with, although I think that their makeup, while good quality is bought more for the nostalgia of the brand (some people haven't been happy with the glossmiers and the lip products, I thought they were good though.). Dior is 100% worth it, in my opinion--I've been super happy with all of their products.