My impression is that you can find successful game viewing at any time of year. In April, the Great Migration (which is typically of great interest to travellers) can be found in the very southern portion of the Serengeti. A map is at this link: http://www.audleytravel.com/index.php/features/greatmigration/gm-map/ (and every time I google it to answer this question I find a different map! This one is pretty cool, though, and I have bookmarked it this time).
April is the rainy season, and from what I read (I went during dry) the grasses can be higher (harder to see certain animals) and the animals could be more dispersed because there are more water sources (fewer water sources means animals are concentrated in certain areas in the dry season). I don't know, but it seems like if you go where the migration is, you'd still have viewing success. I don't know if the rainy vs. dry season advice applies equally to northern circuit parks and southern parks, also.