It's a bit different when it's personal. Consider the significant divide in authority between "we didn't do it like that in my day" and "your mother would never do that." Or, in employment terms, the hero/legacy hero relationship is a boss/employee one, basically; Kid Flash sidekicks for the real Flash so he can become the real Flash, Natasha Irons works in her father's shop until she earns the armor, etc, which means the difference is between the JSA being older coworkers of Diana's (seniority of experience) and the JSA being coworkers of Diana's boss (seniority of hierarchy).
Now, Diana is a princess, so she's used to being in authority over her mother's friends - not much is going to impress someone who outranks Phillipus - which means it's not quite as big a deal for her on an in-universe level. But in a meta sense it still drags her down a peg (in a way which, significantly, Bruce and Clark are not).