It takes immensly long for them to westernize because of the amount of monarch points you need ( = save up ) in order to do so. Also for each 15 basetax that you have you'll will be drained one less monarch point ( normally 15 - for every 15 basetax it reduces that monarch point modifier though - so it's then 14, 13 , etc. ). On first sight this seems good because you don't lose as many but since you'll need 5000 this can mean that you advance very slowly in westernization. Which then in turn means additional high revolt risk and advisor costs for more than you'd imagine - also constant rebellions or religious unity problems if you choose to convert to the Christian faith group ( Catholic / Protestant / Reformed ).
The problem being here that it should reduce the monarch points drained for each 40(!) instead of 15 basetax and that seems to be a bug currently. So you'll have it even more difficult than you should have. This can result in insanly high westernization processes. Let's say you have 75 basetax until the colonial nations like Castile, Portugal and England arrive. You'd then be down to 10 points per month. So since you only spend 10 points on your 5000 limit, you'd have a 500 month process - 40 years and up. And that's being on the low end. Even with the original 15 point drain you'd look at 30 years and up. Now imagine you'd have more territory which is entirely possible and you'd look at 60 years and more. Keeping your nation stable over such a long time is quite a challenge to say the least.
The rebellions will drain your manpower because you'll need to fight the rebels. You'll either lose prestige or legitimacy constantly because of yearly events for the whole duration of the process. It comes down to "less prestige / legitimacy --> more revolts and repeat". Generally it's considered one of the most difficult westernization processes currently in the game if I understood the current forum consensus about it.
I tried it once with these changes to westernization. I got utterly destroyed. Then again it was my first westernization with the natives after the patch ( and these new mechanics ) and I was just not used to the procedure that is necessary to survive