Ray B has hit the nail on the head.
Basically for those who want a compact rifle which does most of what a 30-06 can do just as well as the bigger cartridge then the 308 is an obvious choice. For that reason it is generally more popular than the 06 with youngsters, women and for use as a bush carbine.
In real terms and with standard loads there is only about 50fps difference between the two at 300m with normal bullet weights, and no animal can tell that difference.
The only real advantage of the 06 is when when using bullet weights in excess of 200gr, which makes it more versatile, but the price is a bigger overall platform which doesn't suit everyone.
The 08 is also more popular with the long range crowd as it tends to be a little easier to get that level of accuracy with the o8 than it is with the 06. The cartridge also consumes less "powder", making it a bit cheaper to run.
Availability and cost of ammo also counts for a lot when it comes to popularity. eg, Over here many people bought 08's in preference to 06's during the 70's and 80's because they had access to "government reloads" (i.e. military ammo ) which they got for free.
As an aside, my impression is that the 06 is currently losing ground over here to bigger calibres like the 9.3 x 62 , 338WM, etc. for heavier applications whereas the majority of people buying new 30 cal rifles are opting for .308 or 300WSM, all of which makes some sense.