They both look like Mirage models, no chrome on frame. Wheels are the most expensive components. The Boston Mixte seller put new aluminum rims on the bike. The Providence bike looks like it still has chrome.
Since it does rain in Beantown and they use tons of road salt, the aluminum rims will provide better braking and won't rust.
You might try to get it for $200-$225, but in the NYC area, I can get $275 pretty easily.
If you do convert the handlebars, save the upright set, because in my experience, resales of mixtes with upright handlebars are more in demand.