So, this may seem a somewhat strange thing, and you may think that this is OBS. However, that would be incorrect - OBS itself is doing nothing different when you change the settings in your game from 30 to 60fps, because that's completely separate from OBS.
So, if it's not 'perfectly' smooth in this particular game, what is it then?
OBS is a video mixer that runs on your GPU, often along with the game. The most likely reasoning behind this is because the game is simply using more GPU processing power than average (either due to its pipeline or due to some graphical setting the game has), and it doubles that when you switch to 60fps, and it's most likely eating in to OBS' performance. This doesn't normally happen from my experience, it really often depends on the game and system, though your system is pretty good, so I wouldn't know for 100% sure without tests.
Regardless, OBS itself hasn't changed when you change your game settings -- the game has, as well as what's happening on the GPU.
Things like heavy anti-aliasing and post-process effects may affect this, because they can increase fillrate dramatically. I would recommend messing with the game's graphical settings and see if any of those things affect it. If this is really affecting OBS in this case, then it definitely depends on what the game is doing in its rendering pipeline.