Definitely threads. Why? The future is multi-core. Almost any new CPU has more than one core or if it has just one, it might support hyperthreading and thus pretending it has more than one. To effectively make use of multi-core CPUs (and Intel is planing to go up to 32 cores in the not so far future), you need multiple threads. If you run all in one main thread (usually the UI thread is the main thread), users will have CPUs with 8, 16 and one day 32 cores and your application never uses more than one of these, IOW it runs much, much slower than it could run.
Actual if you plan an application nowadays, I would go away of the classical design and think of a master/slave relationship. Your UI is the master, it's only task is to interact with the user. That is displaying data to the user and gathering user input. Whenever you app needs to "process any data" (even small amounts and much more important big ones), create a "task" of any kind, forward this task to a background thread and make the thread perform the task, providing feedback to the UI (e.g. how many percent it has completed or just if the task is still running or not, so the UI can show a "work-in-progress indicator"). If possible, split the task into many small, independent sub-tasks and run more than one background process, feeding one sub-task to each of them. That way your application can really benefit from multi-core and get faster the more cores CPUs have.
Actually companies like Apple and Microsoft are already planing on how to make their still most single threaded UIs themselves multithreaded. Even with the approach above, you may one day have the situation that the UI is the bottleneck itself. The background processes can process data much faster than the UI can present it to the user or ask the user for input. Today many UI frameworks are little thread-safe, many not thread-safe at all, but that will change. Serial processing (doing one task after another) is a dying design, parallel processing (doing many task at once) is where the future goes. Just look at graphic adapters. Even the most modern NVidia card has a pitiful performance, if you look at the processing speed in MHz/GHz of the GPU alone. How comes it can beat the crap out of CPUs when it comes to 3D calculations? Simple: Instead of calculating one polygon point or one texture pixel after another, it calculates many of them in parallel (actually a whole bunch at the same time) and that way it reaches a throughput that still makes CPUs cry. E.g. the ATI X1900 (to name the competitor as well) has 48 shader units!