Keep and restore. The benefits of changing them are not worth the cost. You're better off using good weather stripping, a low-e film you can have professionally applied or you can do yourself, and using wood window "treatments" i.e. shades, blinds, etc. The old windows have survived 100 years or maybe only 50 years. That's a lot longer than the warranty on the vinyl windows for which you'll spend oodles, and yet not have the same esthetic results (unless of course you can buy high high end windows that are made with wood and metal, with all the modern improvements and time and or labor is not a consideration. Then by all means, replace.

https://thecraftsmanblog.com/5-worst-mistakes-of-historic-homeowners-part-1-windows/

https://www.forbes.com/sites/reginacole/2018/07/17/dont-buy-replacement-windows-for-your-old-house/#54b768d562c0

We restored the windows in our 100+ year old house. We did all the work ourselves so the cost was minimal. Other than replacing original siding, replacing original wood windows is the single most obvious thing you can do to ruin the original character of your house’s exterior. Replacement windows, even good ones, can be spotted from a mile away. They just never look right.

Wood Window Makeover.

Another vote to restore them. Modern windows are less attractive.

Old, old thread here and don't know why it was resurrected. But, we too opted to restoration in our 100-year-old house. Extremely happy with the result.

I disagree with keeping old double hung single pane windows. I replaced my 100 year old double hung windows with Marvin thermopane windows. My old windows were very hard to open and close even after cleaning up paint in the sliding tracks. The new Marvins open/close really easy and have superb weather stripping. Also the exterior window can be flipped to the inside of the house for easy cleaning. So they are very energy efficient and reduce sound. And they have bug screens.