Though not much had changed in regard to terms of costume between films, the difference of the slightly more sleek symbol and the armor makes us think that Batman has decided that he needs to up his game, both in terms of fashion and fighting, and keep up with the kind of criminals that Gotham seems to be producing at an increasingly alarming rate.
The early, pulp-inflected portrayal of Batman started to soften in Detective Comics #38 (April 1940) with the introduction of Robin, Batman's junior counterpart. Robin was introduced, based on Finger's suggestion, because Batman needed a "Watson" with whom Batman could talk. Sales nearly doubled, despite Kane's preference for a solo Batman, and it sparked a proliferation of "kid sidekicks". The first issue of the solo spin-off series Batman was notable not only for introducing two of his most persistent enemies, the Joker and Catwoman, but for a pre-Robin inventory story, originally meant for Detective Comics #38, in which Batman shoots some monstrous giants to death. That story prompted editor Whitney Ellsworth to decree that the character could no longer kill or use a gun.
In my opinion, one thing that makes Batman so easy to relate to is the fact that he's human, and he doesn't have any powers. He gains the victory over most his adversaries through tactics and smarts. On the other hand, compare this to Superman. While he does have flaws, he's a lot less easy to relate to because he's nearly invulnerable, and only has one true weakness.
The first Batman story, "The Case of the Chemical Syndicate", was published in Detective Comics #27 (May 1939). Finger said, "Batman was originally written in the style of the pulps", and this influence was evident with Batman showing little remorse over killing or maiming criminals. Batman proved a hit character, and he received his own solo title in 1940 while continuing to star in Detective Comics. By that time, Detective Comics was the top-selling and most influential publisher in the industry; Batman and the company's other major hero, Superman, were the cornerstones of the company's success. The two characters were featured side-by-side as the stars of World's Finest Comics, which was originally titled World's Best Comics when it debuted in fall 1940. Creators including Jerry Robinson and Dick Sprang also worked on the strips during this period.