I think it would be rather confusing for the user if they see a waiting cursor during the execution of one task and a progress bar during an other. So I would stick to just one progress indicator.
The advantage of a progress bar is the fact it gives an indication of the, well, progress. Where a waiting cursor like a sand-timer or a spinning wheel can't. So the question is if the remaining time left for the execution of the task is of value to the user.
The progress bar is normally shown when something is installing and it has to do several things. The waiting cursor is normally shown when just one thing is processing, like with submitting a form. It is however, always nice to know how long it will take and that is the cause of perhaps a new trend where the progress is being shown in more and more original ways. This article is a nice example where the progress of submitting is shown with the submit button itself. It might be the solution for you.
This doesn't really answers the question how long the execution time should take before showing one or the other progress indicator. But I think it isn't about the amount of time, but rather the type of execution (like instalment or submit) and the value for the user.