Fixing vs Replacing Old Leaky Windows

I live in a house build in 1914 with mostly original wood windows. We have some giant double hung windows and many with beautiful leaded glass. The problem we have is energy efficiency. Many of the windows let in a breeze so you can see the curtains moving and our heating bill is huge in the winter. We are considering replacing windows but have also read that "fixing" them may be a better option as old wood stands up better over time and we would lose much of the beauty of the old windows if we replace. Has anyone gone down this road? If so, do you have a recommendation of someone who does this? If we have to replace all of them, we would also love a recommendation of people who do a great job at replacing large windows.

Thank you!!