The bullnose edge: It's bad...it's really bad. I don't know a designer that would spec out this edge. To be honest I don't know it is that makes it lack style. It could be that if you go to Home Depot to buy a premade countertop, it will have a bullnose edge. It could be that if you leave it up to your fabricator or builder to choose for you, odds are they will give you the bullnose. It could be that all pop-up subdivision houses and apartments use bullnose edges. Whatever it is, just avoid it.
There are a few different edges that actually look good. I will not get into any edge details here that have a profile, or detail to them. Seventy five percent of the time, I just stick to a square edge. It is clean, looks good, and emphasizes the thickness of the counter. It will not go out of style, and is a lower cost to fabricate. Here are a few similar variations that always work.
Beveled Edge: I cant decide if I like prefer a beveled edge over a square edge, but this is a nice look. The bevel helps reduce chipping. I typically do the width of my bevel less that what is shown here.
Here is a concrete counter with a square edge. An updated clean look. A standard for me.
This is called an "eased edge" (slightly rounded). Again this helps with chipping. Each fabricator's version of "eased" is different. The less rounding the better.
In short, unless you are dealing with a traditional or historic styled kitchen it is typically best to just keep it simple.