If it's specifically regarding engagement rings, my ranking would be:
1. Graff
2. Harry Winston
3. Tiffany
4. Cartier
5. De Beers
6. Van Cleef
VCA has spectacular fine jewelry, but the engagement rings? They're quite ugly and very limited in selection in my opinion... And the fact that VCA advertises its white gold collections such as the Fleurette, Socrate, and perlee as viable engagement ring options?! It's very weird to me. Like, obviously, I love VCA, but they seriously don't have much when it comes to their engagement rings, which look more like statement jewelry. Also, not many options for colored diamonds. All I can say is that I think it would be very strange if I knew someone with a VCA engagement ring.
De Beers is more known as a diamond supplier than a diamond retailer, which is why I don't give it a higher ranking. Plus, I feel that its history as a monopoly has always tainted it with a pejorative context. Still, they're probably better known for having a role in proposals than VCA.
I put Cartier just ever so slightly below Tiffany when it comes to engagement rings. Of course, Cartier watches and high jewelry are exceptional, but I know people who worked at Cartier, and they tell me that Cartier is much less eponymous with engagement rings than Tiffany, which I absolutely agree with. The fact that Cartier actually made a love and trinity engagement ring for its client base really says a lot... To me, it's in the same vein as people who shop for Louis Vuitton engagement rings.
Tiffany is probably the most well-known when it comes to diamond engagement rings, with the Tiffany setting especially. There are lots of styles to choose from, and none of them look too "forced." I also think that it's probably what most people aspire to have when it comes to their dream ring. Also, buying a Tiffany engagement ring wouldn't raise any eyebrows, compared to someone who buys a Cartier love engagement ring. Tiffany also carries an inventory of yellow, pink, blue, green, purple, and orange diamonds that can be specially requested. This year, I learned that Tiffany is selling the one-and-only red diamond it's ever acquired. This red diamond has sat unmounted in a vault for several years, but they finally made a setting for it. Red diamonds are the absolute rarest gemstone in the world. The only other luxury jeweler I know of which has acquired a red diamond is Graff. The thing that drags Tiffany down is its accessibility. Tiffany stores are pretty much everywhere, and the entry cost to get into the brand is low.
Harry Winston is above Tiffany, which I think is self-explanatory.
Graff is above Harry Winston, just based on the fact that Graff offers so many incredible and unique stones. For instance, you can purchase a diamond (D, IF, 7.70 ct) cut out of the Lesidi La Rona as an engagement ring for $1.1 million. Graff is especially known as a purveyor of legendary and one-of-a-kind gems (e.g. the Graff Pink) so to me it makes sense that they're ranked number one.