I've given this a lot of thought over the years. For me, it's continuous for everything unless there is a specific need, such as with PIDs or if I have such an enormous project that running a continuous task will result in too slow of a scan time for the time-sensitive logic. I've yet to run into that second issue, but that is a valid exception and something I would consider for your application.
Some of these have been mentioned, but below are my primary reasons for going continuous:
1. Continuous task has no effect on comms on the newer series controllers
2. I see no point in waiting for another scan when the processor is ready. This slows down system response time, however trivially
3. Asynchronous I/O scanning should be fixed by I/O mapping regardless of using periodic or continuous tasks. It's an unrelated issue.
4. Oneshots between periodic tasks can become nightmarish
5. If you have to add logic to a periodic task, you may have to increase the period to avoid task overlaps.
6. The only negative I can think of for continuous is a lack of consistency in scan time, which has never been an issue for me. What does it matter if one scan is 4ms and the next is 5ms? Still faster than 10/25/100ms or whatever I would have set an overall periodic task to. I suppose on massive plant-wide PLCs, there could be poorly debugged code that could cause unexpected issues if the timing changes, so that may be an application where this is important.
It all really comes down to a matter of opinion.