that explosion effect looks basicly the same as our current one only with with some transparency
the actual 3d models really dont look to much more complex than what we have in ah2...maybe more triangles to make it look a bit smoother but honestly overall the difference is barely noticable (and other than a frame rate hit immaterial at over d-250)
so why does it look so good?
3 Things.
1. Texture resolution
2. Convincing terrains and backgrounds
3. Better lighting effects
The texture resolution, obviously is the first and foremost factor in creating the "looks better" illusion. Its like make-up for the actors in filming a motion picture.
The terrains and backgrounds adds a bit of immersive value, but not by too much.
The third, lighting effects, is even more important than textures. It is probably the largest single factor that profoundly effects whether computer generated polygon images look "real" or "fake".
If you ever visited tochy's webpage(the guy who created the famous virtual films "1942" and "1945"), he has created various CGIs for WW2 era planes.
Here are few examples:

F4U-1

P-51D

Bf109G-10
When I first saw those CGIs, I thought to myself "heck, those are pretty neat scale models." At first glance, I could have sworn that they were good photographs of plastic scale models.
Some of the latest Japanese games available for Playstation2, also prove just how much lighting effects are important for realism. Despite the low resolution screens and largely limited processors compared to PC systems, some of those games are absolutely amazing when it comes to "looking real".
As the movie makers say,
"light makes magic"