You can find the advantages of using high FPS, advantages of using low FPS and comparison between them below.
High FPS is good for:
Death-matching and using bugs like C-Bug, 2-Shoot, etc.
Reason: Game is smoother.
Completing skydive challenges.
Reason: The forward, backward and sideward thrust increases.
Lesser time in taking-off with helicopters.
NOTE: There may be more advantages which I haven't covered here.
Low FPS is good for:
On-foot races like Parkour 1, Parkour 2, etc. and for completing maze.
Reason: The running speed of the character increases.
Flying races, boat races and drag races.
Reason: The sensitivity of steering, rotating, leaning and speed of car increases. Players prefer 23 FPS for drag races because it provides greater acceleration.
Challenge maps like Infernus Paradise, Trackmania.
Reason: The time taken to steer, rotate and lean your car decreases. A good reaction time is necessary for these maps.
NOTE: There may be more advantages which I haven't covered here.
Below is a comparison between high FPS and low FPS in two fields -
Challenge map(TM4) and Swimming.
CHALLENGE MAP(TRACKMANIA 4)
This is a part of Trackmania 4 where you need to wallride.
Using HIGH FPS:
Using LOW FPS:
As you may have observed that my car couldn't rotate much in the case of HIGH FPS.
But I did it with ease in the case of LOW FPS.
SWIMMING
Using HIGH FPS:
Using LOW FPS:
Swimming speed was really less in the case of HIGH FPS.
But swimming speed was great in the case of LOW FPS.
For example:
There is a doctor(low FPS) and an engineer(high FPS). If you ask them to replace each other i.e. doctor takes the job of engineer and engineer takes the job of doctor, will they be able to work then?
Surely not.
Reason: A doctor is good in the medical field and an engineer is good in the engineering field, they cannot do each others' jobs.
Same is the case with low FPS and high FPS.
High FPS and Low FPS both are good in their respective fields. If you use the wrong FPS in a field which requires another FPS then you won't be able to complete it or complete it with difficulty. Game does feel smooth and buttery with high FPS and I really like it. But to complete some things you need to change some things.