Egg shells are mostly calcium, and I would think that it would lower the pH of the soil, which might be good for some trees and bad for azaleas, etc.
Comment?
Calcium is totally ph neutral and dont affect ph at all. The eggs contains calcium carbonate, also called lime. When lime is broken down in a wet and acidic environment it releases calcium and carbonate. The carbonate part helps to neutralize the acidic environment and increase ph. If you have soil ph over neutral 7, lime will not break down and no effect on soil ph at all.
So egg shells will be very beneficial if you have acidic tap water and want to grow alkaline loving species. In this case you will find that egg shells not at all decompose slow, quite the opposite.