In serverside hit detection, the delay is split 50/50 between attacker and deffender, so only if they are both low lag does the attacking look right. If only one is low lag, then it looks 'good' for that person, as they are pretty much seeing what the server does.
In clientside HD, the lag is ALL on the attackers end. They have to pre-empt the position of the defender by the ammount of both players lag combined. This means that the defender always gets hit when they think they are, but the attacker will feel laggy if either player is.
The problem is that in a fight, both players are attackers and both are defenders, so in clientside hit detection, if either player lags, the attacking is lagged for both of them. In serverside HD, only the laggy person feels lagged.
There are more complications than this (security, abuse, packet racing) which need to be considered when deciding on hit detection systems, but that gives the general difference between the two.
