I would feel comfortable having one or two of those rockets ready on Mars when planing a trip to Mars.

Meh
SpaceX still rules
Worst thing is the news creating titles like "Blue Origin has beaten SpaceX" and so on...
both are not comparable, Blue Origin is flying straight up while SpaceX is actually on a way to orbit, so a bit more speed involved.
BlueOrigin achived something around Mach 3(~3700km/h) while SpaceX´s First Stage has to flip backwards and kill all of its horizontal velocity (while doing Mach 5 ~6100km/h)
Oh and the Falcon9 is about 50% taller then the pen..umm..rocket from BlueOrigin.
But as Musks only goal is to make other people and industries realize that this is the way forward, I think he already did a pretty good job.
#1 Watch the movie or the book "The Martian" and you won´t even want to think about being on mars

How much more badass can it get...

#3 that's right and the fact that both companies are from the USA everyone can sleep easier at night when it's just Texas and California competing in a space race as opposed to 2 different countries.

As much money as is invested in this, you'd think they could send Jethro out to the landing pad with a broom so the landing wasn't obscured by all that dust........

there is no competition between countries anymore since countries don't do anything inspiring like this. Instead we are left to the tender mercies of vicious corporations who own all the patents, and co-operate with each other anyway. There is progress but, competition is an illusion.

"The first rocket to fly [...] and then land vertically [...] is now the first to have done it twice." --> BO is taking a swing at SpaceX, eh?

#3, #5: The two aren't really competing with each other, at least yet. Falcon is designed to leave Earth, while the New Shepard is a lower orbit rocket.