Sorry, but what is so good about an assault ship? isnt it just a frigate with some more armor?
It's a frigate with a "Holy crap!" range on its guns
The idea is to shoot things dead before they have a chance to return fire.
For Caldari (which I have focused on)
A normal frigate does have a range of max 10km with its railguns (can't really have the bigger guns mounted). Thus you have to rely on the slow missile launchers, and risk at being shot dead.
A destroyer has a range of around 35 km (my destroyer has a range of 30 km) with its railguns. It means it can shoot for about 15 km while the faster small ships oh-so-slowly try to get into range (in my experience I can shoot down 11 PvE frigates without getting shot at once).
A cruiser (other than Moa) has a max range of around 30 km. The Moa has about 45 km range on its guns. You can use rigs to make this better though.
The "normal" assault ships come in two variations. The shooty version (Harpy for Caldari) has a range (if I can calculate right) of 50 km initially. It means a Harpy will most likely win even cruisers without a sweat (because the Harpy is faster than any cruiser, and thus can be shooting from ranges the cruiser can not return fire from), unless the cruiser gets the "jump" (get closer than 30 km unnoticed). Even some battlecruisers are no sweat (ok, it will prolly take quite a while...) for an assault ship.
The Heavy Assault ship has a range of 70+ km. It will be able to nuke down battlecruisers, and even give battleships a run for the money.
All this in PvE, and from theorycrafting point of view. I am sure these are not viable tactics in PvP, and a reality check may cause some interference with my cool theorycrafting