Crutch envy can apply to an individual who thinks they had it worse than others or a group of individuals that think they had it worse than others.
Individuals who identify with a historically oppressed, disenfranchised, and/or victimized ethnic/national/religious/generational identity and compare it to another ethnic/national/religious/generational identity, with the intent of trumping the others victimization.
An individual who feels the need to identify with a group that was victimized in history, then views the atrocities as a form of rivalry against other victimized groups.
Morally obnoxious comparisons of evil (African American slavery versus the Jewish Holocaust).
"Everyone else is a liar, everyone who claims that their campaign was "the hardest of the entire war." All those ignorant peacocks who beat their chests and brag about "mountain warfare" or "jungle warfare" or "urban warfare." Cities, oh how they love to brag about cities! "Nothing more terrifying than fighting in a city!" Oh really? Try underneath one." Emil Renard, World War Z is group crutch envy.
Al Sharpton's anti semitic rants stems from crutch envy