I have a few trips this year in July and August. I have a choice between booking with Concur and booking on my own at AA.com and getting reimbursed. These would all be standard main cabin fare. The company that is paying for me to fly is not the company that I work for. They will give me a hard limit on the price of each round trip which I have been told is generous, and the price is not an issue to me beyond that. These are all domestic flights.

From this standpoint I would think I should get the highest possible fare that works for my schedule and the routing I would like. I have the Citi AAdvantage Executive Mastercard which gets 4x LP/miles for every dollar spent on it for AA flights. I cannot imagine a world in which it would make sense for me to use Concur to book unless fares really are legitimately 4x higher than they are through AA.com. I would accrue my base miles/LP plus multiplier for EXP on the flights themselves (not the cost of booking) regardless of who books.

Is my thinking correct here - specifically that I should book myself through AA.com and maximize the fare within my allowed total for each trip if my goal is to maximize my LP and mile haul for these trips? Would there be any advantage to using Concur here? Better coverage and help in the event of IRROPS? Trying to think through what would be most sensible.