Yes, no, probably, probably not... depends.
Ok, you have two questions here. Yes, a 60fps clip will have more frames per second, pretty self-explanatory.
But the other question is pretty subjective.
In real life (Not real-time), it can be a total disaster, for example, if you are working on a music video clip where dancers were shot at the wrong speed given a specific beat.
Another case would be where you need to fill a specific timeline with the clip, and having fewer frames could not be enough to fill that space.
But if your clip does not have a specific element that can be timed accurately, it does not matter, because our perception is not that exact. It can be just a cool moment in our video.
Even better, modern programs have some neat features to re-warp the frames, it invents new frames with the information on other frames. So, now days is a lot easier to adapt slow motion and time warp clips in the videos.