Personally, I like to think of Divers as the Glass cannon destroyers.
Most Divers can pretty much burst down the glass cannons with 2 or so offensive items. (Usually something like TF, BC, BotRK, or the like) And once they have those offensive items, they won't need any more since those glass cannons won't build any defenses.
And while you start building those defenses, you become even harder for the glass cannon to deal with, because your harder to kill, and the Armor cut's down on LS sustain to you become even harder to duel. Though at the same time, your two damage items do less to tanks, because your not building more damage or armor shed. (Hence their damage "falls off")
Now how does this compare to Assassins? As a class who focuses almost entirely Burst, They might have a better chance of killing mid defensive champs like divers, but that's offset by the fact that they are also glass cannons. Also, an Assassin's mobility make them better at roaming I think.
That said, Divers (in principle) I think tend to be the Best Junglers. Their damage/defense ratio gives them good clear speeds, and with their knack for single target lock down, gives them an advantage when ganking. (Also cause many divers spike in the early/mid game)