Google has been "playing catch up" for a decade now. They also pay less than Amazon (source levels.fyi)
I have heard people claim that Amazon pays more and by that they mean that if you hold your Amazon stock until vesting, it appreciates so much that it ends up being worth more than whatever the Google grant would have been worth. But then you have to ask if the relative performance of the stocks will remain stable over time despite having changed recently, and factor in differences in employee churn and so on.
that $350k base limit is top of the band, not everyone walking inside the door is going to get that. A friend of mind got an offer from AWS about a month ago, his base was offered $180k