Megadeth was formed after frontman Dave Mustaine was asked to leave Metallica back in the early 80's.  There was bad blood for many years (and still might be) but both bands went on to be very successful.

Megadeth never quite achieved the mainstream appeal as Metallica, but except for one album, the maintained their Metal integrity for the most part.  They started as a thrash band and continue to this day with a more traditional Metal onslaught.

Here's the very first video by Megadeth that really explored Mustaine's love for current events and politics.  From 1986 it's "Peace Sells... But Who's Buying".

Thrash Metal continues to thrive around the world, even in the good old USA.  "Lich King" is a good example of the underground Trash Metal that is still alive and well.