Regardless to what you do in your current situation, a certain amount of money throwing around is going to need to happen. There isn't really a "just switch from Pop's rosin to Oak Soft" type answer that is going to make your two bows become one, but there are a few things you can do.
Depending on how long it has been a rehair isn't a Silver Bullet solution, but it can help on both fronts. Otherwise if you have a bow maker in your area, get in contact with them and let them know what you are experiencing. They might want you to bring both bows so they can see what you like about both of them, but they will likely work on the bow with the good sound, not the good feel. It is extremely difficult to change the sound of a bow, (especially without altering the playability) but you can significantly alter the playability of a bow without much change in sound. If your bow is tip heavy and light, there are ways to add weight to the frog end of the bow, which will bring the balance point back into your hand making it easier to play. If there is a camber issue, in most cases that can be addressed as well.
Various costs will be involved depending on what you wish to achieve and what the bow maker recommends. You might have to pay a "bench" or "appointment" fee for the recommended consultation, but the bow maker should be upfront about that and what it will cost. While it is entirely up to you what you are willing and able to spend, they should be able to give you realistic expectations as to what they can do. If you really like the sound of your bow that isn't playing the way you want it to, this is likely your best option.
If that doesn't yield the result you are looking for or unfavourably tips your personal cost/benefit scale, you could be back in the bow shopping game. Not a lot to be said on that front other than try as many bows as you can for as long as the makers/shops allow, and hopefully you will find Goldilocks.
Best of luck.