How do turbofans and piston-engines compare in terms of maintenance costs?
Your question has some areas that depend on circumstances, models, etc. but to answer in general:


Piston engines are generally fully overhauled every 1200 to 2000 hours or so. Time to overhaul one varies with the engine model, and where the overhaul is done, as it can be done at the factory, at a repair shop, or by a qualified A&amp;P/IA (a field overhaul). A piston engine overhaul can cost as much as $25,000 or more. 
Turbofan engines will likely not require major service during those 10,000 hours. Most turbofan engines are inspected regularly and continue to operate on condition unless manufacturer recommended time periods are reached or exceeded. Time to overhaul varies greatly by engine model. Costs vary greatly as well, but in the case of turbofans you're talking in the hundreds of thousands of dollars.