I do believe that what is in the soil has an impact on the flavor of the tomato. I have personally experienced the difference in tomatoes grown in soil that was almost entirely compost, vs. soil which is not quite so rich. I think the addition of compost is the single biggest improvement you can make to your soil, and by extension, any of the ingredients that go into compost such as coffee grounds, egg shells, apple and carrot peels, etc.
I do also use pelletized organic fertilizers as they provide a convenient, balanced mix of nutrients that would take endless measuring and testing if I tried to replenish entirely with compost.
I think the addition of egg shells may not provide quite the benefit you are thinking of -- I speak of the old adage that egg shells will contribute calcium, eliminating BER. BER is more complex than that, and egg shells aren't really the silver bullet. however strictly as a soil additive, egg shells are just fine.
If you are looking for what ingredients work best in making compost, there are many websites as well as an area of Tomatoville dedicated to the subject. You don't have to have a compost pile to produce rich soil. Lasagna gardening is the addition of compost-friendly ingredients in layers in late fall and allowing them to blend and "settle" during the winter so that by spring, you have rich soil.