And how to estimate the amount approximately?
You cannot. Most of the earth is water, and fauna diversity is highest in water. We are still tagging and tracking the movement and reproduction cycles of animals, and that is a never ending task. I say we cannot reach an accurate approximation because of how these projects work. They are targeted towards the monitoring of specific species. Next, different countries have different approaches towards conservation of the same species, and above all this many countries choose not to report numbers. The example which comes to mind is the Red panda. As many animals come inside the radar of active conservation efforts, even more remain outside it.
In fact, some time ago I read a compelling article about why the WWF should change their logo to a Red panda (or known as the lesser panda) rather than the giant panda, the argument being that awareness about the giant panda is very high while red pandas are still misunderstood as pandas. Unfortunately I cannot find that article now, but you can visit the red panda network to find out more.
Which has the greater amount on Earth?
Second, what do you consider as a wild animal? are insects included? are gutter rats included? Is the infestation of wild boars near the now defunct Fukushima plant included? If yes then they outnumber domesticated animals by a long shot. I would dare to say that cities are habitats more for members belonging to Animalia but not belonging to Homo.