usage of 'more common'

If you used 'more common', I would take it to mean that tigers occur with greater frequency in Asia than Africa, but that they do also exist in Africa in some capacity. The 'more' in 'more common' is the difference between the two things being compared - more completely I would understand the sentence as:

While tigers are common in Africa, they are more common in Asia

Since tigers don't live naturally in Africa (it wouldn't surprise me if some where there as pets), 'more common' is probably not the correct phrasing. Generally people would understand your point, in fact many probably incorrectly assume that tigers do exist in Africa anyway, but I would avoid using that phrasing.

If something is common, it is found in large numbers or it happens often.

Since tigers are not found at all in Africa, it is erroneous to say that tigers are "more common" in Asia than Africa.