Depends on what functionality you want to expose.
Your objects cannot contain your business logic, your processes do. So if you want to expose small actions without any business logic your objects can do that, but you should try it first, because you would need to initialise it before calling, think about sessions logs for the calls, license considerations (when you run multiple web service calls) etc. And obviously since the objects should not contain business logic, then the application which calls it should be the one which does the business process bit.
If you call processes, the complications are less, but of course the process would need to contain the required functionality.
The difference between them, would probably how you call them (initialise, license etc) and calling a full functionality vs calling granular building blocks for a functionality.