http://answers.ea.com/t5/Battlefield-4/IMPORTANT-Updated-11-10-BF4-Beta-Known-Issues/td-p/1600897
scroll down to "Known PC issues," in bold "We have received reports of Freezes and Crashes affecting the BF4 Beta client. Our team is currently investigating this matter and we will update you here as soon as we know more.
If you are affected by a Freeze or a Crash upon joining a game, and the error message “BF4 Beta has stopped working” appears, please make sure your Windows is fully updated and your Graphic card is running on its latest driver. Alternatively, some players using GeForce drivers were able to fix this by downgrading their driver to an earlier version. "
It is a known issue, I wouldn't point to your hardware yet. If you want to test if it is your hardware, download a benchmarking software, like msi komburster, set the settings to high, and just let it run. If it isn't crashing, it's not your card.