Concupiscence differs between Catholics and Protestants primarily in the terminology and interpretation.
Essentially, to remember it, you have to know Latin. Think of "con" as with, cupire (or cupiere, my spelling may be bad) is the meaning of want, just think of Cupid and you'll have no problem with this, and scence is the state.
So basically Concupiscence is "the state of wanting sin" (I've never seen the cup- verb used without some negative implications, though Cicrero's rants about Catiline probably don't do any favors to his opponent anyway), and the core difference in the theology of concupiscence revolves around original sin in most cases (or so it seems, again, Protestants vary widely, so I speak from a specific background rather than categorically for the whole). Wikipedia is really a great source of information on this debate, but to sum it up:
Catholicism (at least at the time) teaches that the original nature of man is good. Protestantism teaches that the original nature of man is evil.
For Catholicism, because human nature is good, even though humans are not corrupted by sin they only fall into sin when they commit an action, rather than thinking about it. For Protestantism, the focus on the inherent evil in mankind means that even contemplation of actions that are evil with the intent to commit them (for instance, lust) is in and of itself wrong, even if the act is not committed. because it is a manifestation of the evil within the nature of a person.
Protestants believe that concupiscence can never truly be eliminated, but sanctifying grace can play a role in turning it around. Catholicism does not consider contemplation (with intent) of sin wrong, it is the action that makes up the sin, not the thought.
Part of the reason you don't see much on concupiscence in Protestant traditions is that many Protestants consider it itself to be a sin; from my enrollment in the Nazarene church and a nondenominational Protestant church, I can tell you that at least in the more "conservative" groups it is definitely considered a sin, and even in some of the more mainstream ones as well (for instance, a passage is often cited where Jesus compares looking after a woman and lusting in one's heart to adultery, which is the background for the Protestant theology on the matter).