[bookwormAT]

Flash does not use any battery power at all, except when you choose to use a flash based application.

The stock Android browser has the option to load plugins on demand. That is: no flash application is loaded within the browser until you click on the application to enable it. The same is true for memory usage or bugs.

I don't think there are any advantages a browser without flash has over one that supports it.

[swombat]

A great many webpages have Flash adverts, so if you're browsing news sites, etc, normal sites that people do browse, you will probably end up being served Flash and so your battery will drain.

[bookwormAT]

Again: not a single one of these adverts will load when you visit your website. You will see grey boxes with an icon on Android, similar to what you see on iOS. There is no flash running that could drain battery.

On-demand flash support means that you can touch one of these grey boxes, and only then will flash load and execute the application.

[jonknee]

Only if you go out of your way to load the Flash advertisements.