One major difference is the aims of both. In law one is seeking to establish 'justice'. This overall aim often involves the judging of the individual and the conclusion of either 'guilt' or 'innocence' based upon several factors outlined by the prosecution or defense. The cases of law by their conclusion have to bear all the attractive hallmarks of simplicity even if the cases themselves are difficult to judge.
Those working in law judges, barristers, etc often don't have the luxury of time to deal with every nuance within a single case. Time constraints and the number of cases to be judged render it very difficult to give each case its due.
In psychology, one stays as far away from judgement as is possible with the researcher who is prone though aware, of the cognitive biases which may influence thinking. Those working within the field of psychology understand gaps in knowledge which naturally occur within any scientific field. In psychology, there is no time constraint as such unless funding issues are of concern. If one researcher dies the work may carry on through other researchers who continue the work and the scientific corpus of knowledge grows.
A key similarity is that both law and psychology seek to understand. In general terms, however, the law is concerned with understanding the events of a single individual or case. Psychology has nothing short then understanding all of human behavior.