I did a couple of testes and here is what i found out.
Output to MP4 doesn`t give you video file at 60fps
Output to AVI give you video fil at 60fps regardless to you in-game frames but my video editing program creates audio video de-sync if I render using AVi files
If I may pop in with a couple of ideas, when audio/video de-synchronization occurs, try using PCM ("Uncompressed") Audio with the AVI container. It is very lightly compressed, but for the most part it is considered 'uncompressed' and is the most compatible format for all audio editors and video editing programs. It may help alleviate the de-sync and although it is higher filesize, is faster for capturing as well (less compression/calculations going on).
Also, with the AVI wrapper, be sure to set the Keyframe Interval to "1", to ensure editing compatibility with video editing applications [you do not need this setting if you are using the MJPEG codec]. It will create larger files (recordings) as there is less room to 'analyze and compress' where the codec can, but it should also help with any desynchronization problems.
I found the new implementation of the MP4 container in Bandicam able to record up to 120fps smoothly, and I have a slightly lower performing CPU than you do:
http://cpuboss.com/cpus/Intel-Core-i5-3 ... MD-FX-6300
Are you getting over 60fps in the game, before you try to record 60fps?
If I lower the in-game resolution of Battlefield 3 (and lower some extra effects as well), I can get over 100fps and when I record in 120fps MP4 in Bandicam it comes out looking very nice and smooth then.
[The MP4 wrapper, as configured by Bandicam, seems to utilize VFR or Variable FrameRate, so if I look at the media info for the MP4 recording, it shows a "Minimum Framerate" and "Maximum Framerate", where it will lower the framerate for lower motion scenes and increase the framerate for higher motion scenes (high-action/movement); but the Maximum can indeed be over 60fps, up to the 120fps limit set within Bandicam - I will include a screenshot of the Mediainfo data from an MP4 below]
Sticking with the MP4 container for a moment, you also could try setting Bandicam to record at a lower recording resolution (for example, play the game at 1080p but tell Bandicam to record at 720p
) and see if that helps. Or, you could lower the in-game resolution (tell Bandicam to record Full Size, but lower the game resolution to say 1366x768, for example), which should also help to increase your in-game fps.
These are just ideas to start with - but it may help start you out finding where the problem lies, with your inability to get 60fps recordings... Good luck with it!