Personally, I would give 2012 the edge and I can tell you exactly why.
They are both pretty bad films...............but 2012 at least has some lavish and well done visual effects sequences (driving through a crumbling L.A in a Town Car may be hilariously stupid but at least it's top notch CGI rendered with results to boot that you see) to watch around the cringeworthy dialogue and poor performances. It's also properly shot without all that close-up shaky-cam nonsense. Which in Battle: Los Angeles was, I believe, quite intentional.
At least 2012 has some CGI-yumminess.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist