Darth Subjekt
The beginning of the end.
This is stupid. in the movie, there wasn't some magical being or voice that said, "only use sabers!" There was nothing to keep Dooku from trying to outright pwn Anakin with the force, except Anakin who jumped in his shit and pwned him right off the bat, fair and square. And we've had that debate more times than I care to recall, and Dooku was simply outclassed and beaten by a superior Anakin. Now you can wrestle with the semantics of that all you want, but Sidious (as far as canon by GL's own words) never told Dooku to hold back. There is no point in "testing" someone if you're not going all out on them to see what they can really do. He may have said if you get in trouble I'll help, but GL never said that and it still doesn't mean for Dooku to go easy on him. That would simply not make sense.
And age has NOTHING to do with the fight. Read the ROTS novel, it describes it there i believe. It says something along the lines of him being completely revitalized before his encounter with Anakin. Ask Ox, he's the biggest Dooku fan around here and he knows the exact quote. And he even admitted to the reason why he lost.