A great tool for this, if you don't want to use a Sawzall, is a Crescent
Suregrip No. 56 Nail Puller

Eh, I find older nails in older wood don't want to come out with that sort
of tool.

I use mine all the time, for, e.g., removing deck boards without all the
sawdust, noise, and mess of multiple sawcuts.

Yeah, they're handy but they're pretty much a single-purpose tool. Most
folks would be better off having a tool they can use for multiple purposes.
Like a sawzall, a shop-vac and various drywall repairing tools for when the
"Destroyzall" goes wild... grin