Helping poor people is extremely hard. I am pretty confident that going to Mars is solvable by just throwing enough money at it. Solving poverty for more than a very breve period is much harder.
There was an episode about the problems the Millenium Villages project was encountering (http://www.econtalk.org/archives/2014/01/nina_munk_on_po.htm...) and it just made clear how many problems there are to overcome that you just don't consider. I am not saying it's unsolvable, but it's harder than traveling to Mars or making a self driving car. So Elon is the safer bet.