Dichotomize or not? Logistic vs Linear

[FallenApple]

Say I want to see if a continuous variable, say strength, is associated with another continuous variable, say height.

Clearly I can just use linear regression with height as the response variable and strength as the predictor variable.

But I can also split height into a tall category and a not tall category. And then do logistic regression with the log odds of height as the response. So what is the advantage of one way vs the other?

 

[Dale]

Do you want an estimate of the odds of being tall or do you want an estimate of the height?

 

[FallenApple]

Do you want an estimate of the odds of being tall or do you want an estimate of the height?

I guess that's the confusing part. What should I do if I want to know if strength is in any way associated with weight generally?

If I do linear regression, I can interpret the change in mean height for unit increases in strength. But for the odds, I can do the change in odds of being tall for every unit increase in strength. But either way, wouldn't either give an association? If on average, height increases when strength increases, then I would be surprised if the odds didn't increase as well.