How to compare these two numbers?

Dec 2015
935
122
Earth
Compare \(\displaystyle a=\underbrace{99^{99^{99^{\dotsc }}}}_{99!-times}\) with \(\displaystyle b=\underbrace{99!^{99!^{99!^{\dotsc }}}}_{99-times}\).
 
May 2013
94
10
Code:
the best way is to start small, and increase it to see the trend.
2^2.          2!^2!
2! times    2 times. here they are both equal.
3^3^3...                           3!^3!^3!
3!  times                             3 times.
which is off the chart, |  which is quite large, but not as large as 3^3^3^3^3^3
so a is bigger.
 
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