I would'nt doubt the power of Toyota Avalon, and may well be also in the league of the full size cars and not a direct competition of this car.
Acura RL will also be NOT a direct competition of Maxima, as Nissan has its own Luxury line, Inifiniti (Nissan's luxury division) Q45, I30 and G35, that compete with Acura line up of Honda's luxury division and Lexus line up from Toyota.
Altima has been an in between Go Getter type of model of Nissan, and they really did not explore its full potential till recently.
In the past and still, from the 1980s onward, when Maxima first came on scene, it was established to compete with Camry and the Accord, and it still is made to compete with these two cars. In terms of styling, and mainly under 30K price range for the base models, which the Camry and Accord are.
Accura RL is a pure Luxury sedan made to compete with Lexus's ES and GS, and Nissan's Infinity G35 and Q45, which are all above $30K range (a main start up range for the entry level Luxury sedans).