I have experience with both. I have an old Californian Bungalow. I have removed extisting period doors and had them dipped, this quick easy but the timber often comes back a little worse for wear.
I am now refurbing my double hung windows for my new baby. After getting some advise I found the best way is to use a heat gun and a scrapper. This sounds like an unpleasent job and it is, but as long as you keep the room well ventilated and wear a mask while stripping the paint you will have a really good finish at the end. After all the paint is stripped(there will always be a few speckles left) use a mild paint stripper sparingly on the timber , have 2 buckets of water handy one with a pot scourer the other with a cloth of some sort. Use the scourer lightly on the piant stripper after a few minutes and run the wet cloth over after that. You will be left a fantastic finish with the timber so smooth that sanding is not required. A light touch up with a dark stain will complete the job.
Yes this is a big task but the results are well worth it. I have now started the old Red pine skirting and the fun continues.