Yes, cushion cut diamond engagement rings have been popular for a long time and remain a popular choice among engagement ring buyers. The cushion cut is a classic and timeless diamond shape that has been around for centuries and has remained popular despite many changes in fashion and style trends.

Cushion cut diamonds have a square or rectangular shape with rounded corners and large facets, giving them a distinct, vintage-inspired appearance. It is well-known for its brilliance and fire, and its distinctive shape can make it appear larger than other diamond shapes of the same carat weight.

Cushion cut diamond engagement rings have become especially popular among celebrities in recent years, with many high-profile engagements featuring cushion cut diamonds. This, understandably, has helped to increase the popularity of cushion cut diamond rings with general consumers.

Overall, cushion cut diamond engagement rings are a timeless and elegant choice and aren't going away any time soon.

Cushion cut diamond engagement rings, or cushion cut diamonds in general, have several unique characteristics:

1. Brilliance and fire: The large facets of the cushion cut diamond reflect light in a way that creates a lot of sparkle and shine which makes the diamond (and ring) appear even more beautiful.
2. Unique shape: The cushion cut is a square or slightly rectangular shape with round corners which gives it a distinctive look.
3. Vintage style: Cushion cut diamond engagement rings are often considered a vintage inspired look or diamond cut reminiscent of old Hollywood glamour. Great choice for those that want a classic diamond shape but still want to stand out.
4. Appears larger: The cushion cut diamond often appears larger (when compared to identical carat weights for other diamond shapes) due to its unique shape and large facets. This is a great choice for someone who prefers a larger looking diamond without having to pay as much (comparatively) for a higher carat weight.

Other than the obvious, which of course would be the shape difference between a round and cushion cut (square) diamond, there's a few key differences between round and cushion cut diamonds - especially when it comes to engagement rings.

1. While both are known for their brilliance and fire, cushion cut diamonds reflect light in a more subdued gentle sparkle.
2. Round diamonds are more expensive than cushion cuts due to higher popularity and demand.
3. Cushion cut diamonds will appear larger than round diamonds of the same carat weight due to the larger surface area and unique shape of the cushion cut.