It is very much a judgment thing on the day, and depends on a lot of factors.
Some situations are no-brainers such as an uncontained fire or extremely critical medical case, but in a lot of others it's going to be a decision by the commander depending on the nature of the emergency and the conditions at the field (WX, runway length etc.)
For example, if I had to shut down an engine due to an oil leak, and the other was running fine, I'd be happy to take the time to jettison, whilst keeping an Eagle eye on the good engine, and putting myself in a position where a quick approach could be made if the other one developed problems.
If I just had an unexplained flame-out, I'd be wondering about contaminated fuel, and probably opt for an overweight landing, field conditions allowing.
On the 777 the OW landing C/list simply instructs you to check the landing climb limit, and gives you the option of a flap 20 landing.
It should also be noted, however, that in an overweight landing, it's not hard to melt thermal plugs, and braking should be used with that in mind.