What happens if you have more FRAMES/SECOND than 25?

Isn’t that better? Doesn’t it make the video smoother?

Yes that is correct. TV has a higher frame rate but each frame is half resolution, yeilding 2 fields per frame. So the movement appears smoother but the image is less sharp. If you make an animation at a higher frame rate then it will be sharp (no fields) and smoother to playback, BUT the data rate will go up for the extra information you need to play.

That is why DSLRs often have higher frame rates but at lower resolution scan sizes. eg. 720p at 50fps. but 1080p at 25fps

I’d say it really depends. It’s certainly better if you have to shoot a fast moving subject because it will look blurry. Or if you have any other type of fast/rapid in frame movement. It’s also more appropriate for all sorts of shots where the camera is moving, horizontally or vertically.

In almost all other cases you will not be able to tell the difference and you will end up having bigger files as 3point already pointed out.

Problems start when you want to play back 30 fps on a PAL system though. I’d say in theory more frames is better for smooth rendering of movement, but check the playback context before you go off sequencing rendered stills to movie formats at 60 fps.

organic is right on the money. Always plan your frame rate to best suit your principal playback venue. The benefit of using a higher number of frames rendered for each second (rendered FPS) can be offset by having to interpolate for a lower playback FPS – some methods result in choppy animation because certain frames must get dropped, and it may not be in a consistent manner. For projects where a number of playback FPS values have to be served, it’s possible to jigger the rendered FPS for a single animation/range of frames by using Render>Time Remapping (the most versatile and cleanest method in terms of smooth playback), the NLA Editor or, in some few cases the VSE.

I have to do a fair bit of work that is (still…) targeted for dirt-cheap NTSC (the standard in my country) video. (Yes, it is a deliberate choice to accommodate cheap and readily-available playback equipment for exhibits and so-forth.) Consequently, the things that I therefore have to consider encompass more than frame-rate: they also include pixel shape and aspect-ratio. Usually the best results are obtained by … biting the bullet and rendering for that target. You have to make sure that Blender is set for the proper target settings and you must pay extreme attention to the “safe areas” that are indicated, and even then you must pray. Truly, it feels like rendering with both hands tied behind one’s back.

However… it does also force you to economize. Since you have so very little visual area to work with, such low effective resolutions and such questionable color rendition, there’s zero room for subtlety. You constantly have to burn to an actual videodisc, then stick it into the actual player to see what you are actually going to get, and you have to do that before you do the final render. (Blender’s “preview render” capability is a god-send.)

To answer the immediate question: if your media has an “inherent” frame rate, as does PAL or NTSC, you should render to match that rate exactly. If you want to render “on twos” or whatever, choose either “on twos” or “on fours.” Not something that will be a peculiar mathematical multiple. It just won’t be satisfactory and it is therefore a waste of time. If you don’t have an “inherent” rate, then I would simply choose what looks smooth to your eye; as low as you can get away with; nothing higher.