In connected mode, the block reward is spit among currently-connected nodes only, according to the hash/s that they were contributing at the time.
It seems easier for the server to cheat in connected mode. With contributed mode, if they have doubts, miners can log how many shares they contribute, check how much they gain, and decide whether it's fair. The server could "invent" imaginary shares to keep some bitcoins, but at least you have some hard numbers to check. With connected mode, how would you know if you got a fair share ? What if the server pretends you were not connected when the block was found ?