Why is there a difference between military parachutes and those used for skydiving?
From what I learned, different types of parachutes don't make them 'old' or 'new'. They are used for different purposes.

For example the dome shape parachute is usually used for static line jump where no maneuverability is really required. They drop vertically relatively to the plane path when air friction is negligible.

The other kinds are usually used for special forces because they always do jumps like HAHO (High Altitude [Jump] High [Altitude] Open) when the location they jump is outside their country's territory, and infiltrate by air so the plane is out of the radar/SA missile range. They have to have the ability to glide on a long distance.

Another case is they have to have the ability to change the trajectory or precisely land in the drop zone. So maneuverability is a must.

Size differs for different manufacturer and different specs. Even though the dome type parachute is relatively larger, the chance of getting hit is similar with other types as you don't have much speed and you can't do crazy high G turns. You really can't avoid any attack towards you unless you have superhuman reactions and the sixth sense. 

To conclude, different types of parachutes are used for different purposes in different scenarios.