Look at usage first. What are the number of occupants in each of your homes? Consider water demands AT THE SAME TIME. Can BOTH homes be supplied with sufficient amounts of water? Do you share 1 pump (I doubt it)? But if you do, should you get your own (I don't know enough).
Does your municipality permit you to buy the home KNOWING you have a shared well? If not, the answer is obvious. Whose lot is the well on? Who pays for repairs (and you better have a signed agreement!)? If you end up on the 'wrong side of the well' with your new neighbors, who is controlling the pump? The electric bill too?
Now, suppose you want to get your own well. Will your new well be 'downhill' from the current well (which means you'll be the LAST one to get the water flow)?
To be honest with you, I don't like it. Even if it was my brother sharing with me. Personally, I'd want control, and everything that goes along with that INCLUDING the problems.