Is there a difference in the taste/seeds of egg-sized eggplants, and long and slim eggplants?
The varieties of the 2 eggplants shown in the pictures are not actually given, but to me the long variety looks like the Japanese/Chinese eggplant and the round variety looks like The Indian eggplant. By the way, there are many different eggplants out there. If you want to have a look, check out this: website.

The Chinese eggplant has a thinner skin, more delicate flavour (I think sweeter) and less bitter seeds, although most modern varieties have bred these out anyway.

The Japanese eggplant is very similar and again has a thin delicate skin and sweet flavour.

The Indian eggplant is similar to the American eggplant with a thicker skin, more seeds and a stronger flavour.