Re: Perhaps money will talk louder:
"With Linux, patch gets announced today, I go to vendor site, get patch, start testing, in 3 weeks time I am happy and install patch"
And what about all the other patches that get randomly released in the mean time? At some point in any sane enterprise model you have to test and deploy in managed batches.
"With windows patch is announced today, I wait till the next "patch tuesday" (3 weeks and 6 days in the case of the example)"
They are normally released the day after the outline announcement of impacted products / severities and at the same time as the detailed vulnerability information. There are exceptions but they are pretty rare.
"1 week later am happy"
A common and safer model is to incrementally deploy critical patches after 1-2 weeks of testing, and deploy non critical patches after a 5-6 week testing cycle a month later...