What is better?
1 - assumeFPS
2 - changeFPS
3 - convertFPS

1 - Changes the frame rate without changing the frame count (causing the video to play faster or slower). It only sets the framerate-parameter. If sync_audio (which is false by default) is true, it also changes the audio sample rate to match the duration of the video, the pitch of the resulting audio gets shifted.

2 - Up to v2.05, the video gets truncated or filled up to preserve playback speed and play time (the number of frames was not changed). In later versions, the behaviour has been changed and the number of frames is increased or decreased like in ConvertFPS.
In v2.54, an option linear=true/false is added to changefps. This will make AviSynth request frames in a linear fashion, when skipping frames. Default is true.


3 - The filter attempts to convert the frame rate of clip to new_rate without dropping or inserting frames, providing a smooth conversion with results similar to those of standalone converter boxes. The output will have (almost) the same duration as clip, but the number of frames will change proportional to the ratio of target and source frame rates.
The audio data are not touched by this filter. Audio will remain synchronized, although the length of the audio data may slightly differ from that of the video data after the conversion. This is because the output can only contain an integer number of frames. This effect will be more pronounced for shorter clips. The difference in length should be ignored.


Most time I see (and use) in 23.976 > 25 convertion, assumeFPS, but don't would be better use convertFPS, that keep original movie time, even though it needs to insert aprox. 1 frame/sec (duration 1/25 sec.). Or in case of 25 to 23.976 is just blending 2 frames in one by second, aprox.

Why can't be applied convertFPS to a 29.97 interlaced source in a straight way, without 60ito24p, with a good result, targeting 23.976 or 25 fps.

The Problem in here is already said in its Name "BLENDING".
The most worst case for Frame by Frame or field by field playback.
In Fieldbased Playbacks like interlaced on a 525 or 625 Line TV this wont be recognised. But on progressive results it will be recognised as ghosting/blending.

In interlaced to interlaced conversions that can be done. But on Progressive sources you wont gain anything as 23.976 to 25 using just a pitching of sound . That soundpitch can be avoided using a transformation of the sound if really wanted.
The Professional Film industry also doesnt apply fieldblended conversions, here also the pitchup is the prefered method.

Same here: We first do "interpolate" the 29.97 to 23.976 progressive as a direkt 29.97 to 23.976 using convertFPS() will result in Blendings at the final 25.000 target.

The professional way is to avoid blendings if possible.

wasnt one of those deprecated?

No.
http://www.avisynth.org/FPS