Are young researchers at various universities held to the same standard? Let's say that Candidate A is at University X, working in the same field as Candidate B, who is at University Y. University Y has lots of faculty working in that area, and an active seminar. Candidate A collaborates with one other faculty member at University X. All the top mathematicians regularly give talks at University Y, which is considered top 5 in that area of academia. Candidate A is hard-working and  just as driven as Candidate B but doesn't get to interact with scholars as much as Candidate B. Candidate B has an easier time with research than Candidate A as a result, and publishes more papers of better quality than Candidate A. 

When hiring committees or program directors judge Candidates A and B, Candidate B comes across as better, although Candidate B had a lot more advantages. Are those advantages considered when it comes to getting grants or job interviews? Or is it basically a losing battle for Candidate A?
I don't think you are asking the question that you think you are. If you are asking whether the two will be treated equally in the hiring process only then the answer is that the B probably has an advantage in any situation in which they are the only two candidates and all other things are equal. But all other things probably aren't equal, even including personality and flexibility. 

Also, it is entirely possible that A has written an especially strong dissertation and has a great record otherwise, while B has been allowed to coast along a bit in the shadow of the senior faculty.

Also, candidate B can't hold "every" position, so once they (maybe) grab the plum job all the others are still open. And as stated above, the "plum" candidate may turn out to be a "prune" instead. 

I assume you ask this because you think you are more like A than B. Otherwise I don't see you asking the question. Like anyone, you need to make your best case for success in anything you apply for. Do the work and make it count. Then you will be taken seriously, even if B is still lurking. 



But the title question is different, since you said "at the various..". There the answer would be probably not as what is typical treatment at one place probably varies quite a bit from others, except in the most generalized terms, such as time to tenure. If you meant "from the various..." instead, then ignore this note.