While Peter's response is correct I don't think it answers the original question. Peter is indicating physical properties you need to be concerned with for a given application type but he really doesn't get into what drive class you would want to use for each of them. And in reality that is a very application specific decision with no real clear-cut answer. Much of the decision has to do with relative performance level of other components in the system.
For example, with the components available to him and their relative capability distribution, Peter would very often use torque amplifiers for his applications. His motion controller is the most capable component in most systems so it makes sense to consolidate as many motion functions into it as possible. If the drive being used in that same system had a very high bandwidth velocity loop and had some good dynamic tuning tools Peter may opt for velocity mode operation.
As shooter alluded to, not all applications require all physical control capabilities. Not all applications require positioning so the positioning function is not required. If your application doesn't need positioning your drive certainly doesn't need the positioning function. However, even if positioning is required, it doesn't mean you necessarily want to use a "positioning" drive. Be EXTREMELY careful with "positioning" drives, by the way. The difference in capability across the available choices is truly staggering. If you have an application that requires torque/force limiting then you need a drive that has torque control capability. However, where that torque/force limiting function resides is, again, a separate design decision. The function could reside in the drive or in an external controller. If torque limiting resides in the external controller a drive that accepts a torque command would be required. If the torque limiting is performed in the drive then the drive could accept either a velocity or a torque reference.,
As you can see, this is not necessarily a component level decision. It is a system level decision. Some of the choice lies in your personal decision about who's hands you choose to lay your chances of success in.
Keith