Why the Torah favors the oldest (not the older) son in some areas is a conversation in itself.AFAIK none of the Rishonim say it is because the Bechor is inherently more destined for greatness than his younger siblings.
I've heard people discuss this question of why the younger brother frequently does better in Tanach but I no longer remember the reasons given.
However, it can also be explained with simple statistics. There simply are more younger brothers than there are oldest brothers (bechorim) so the odds are not in favor of the bechor being the most successful brother.
To address some of the examples given here:
Yitzchok was the son of the Soroh, Yismoel was the son of Hagar.
It is questionable who was the bechor Yaakov or Esav.
Yosef wasn't the biggest of the Shevatim according to the Gemorah.
Menasha and Ephraim was a 50/50 chance of who would be more successful.
The Meforshim give many reasons why the redeemer of Klal Yisroel had to grow up in Pharos palace. Had Moshe been the one born first he would not have done so because he wouldn't have been put in the Nile as the decree to kill male children was not in place at the time of Ahrons birth.
The difficulties Dovid had in growing up led to his greatness. He was the only son of Yishai who had those difficulties and it was because he was born latest that he had them.