Some of the adaptive approaches to developing systems (like agile) are becoming more popular. Are they better or more appropriate than the prescriptive approaches in most cases? Why or why not?

Adaptive approaches have their uses, but the primary problem with them is that they don't ever release a finished product; the resulting system or program is constantly in a state of flux with new versions, patches, updates, or miscellaneous bugfixes. The project is never really done until the company decides to stop supporting it at which time it is abandoned and a new one is put in its place. A more prescriptive approach on the other hand has a set release; it is finished and released to the customer at which point the company only has to maintain it. These issues don't, however, make either one better or worse than the other one; it all depends on the situation. If the situation calls for the product to be out there now regardless of any bugs that don't make it completely unusable, then the adaptive approaches are better. However, if the situation calls for needing to release only the complete package for some reason (such as maintaining standing with a certain client) then a more traditional approach (such as the waterfall methodology) would be appropriate.

Basically neither one is better than the other; it is simply a matter of whether you have time to produce a quality product or the customer wants it now regardless of issues.