Why Use InputManager over the easy transform.Translate?

There's a very big difference between the two. In fact there's almost nothing similar between them, this is like comparing apples to sea urchins. InputManager is a system that records key presses from your keyboard/controller, whereas Translate moves a GameObject. What you're probably thinking of is "Whats the difference between transform.Translate() and Rigidbody2D.velocity"

In your first example (using translate) you can only move in one direction, and at a constant speed. It doesn't use physics but instead updates its position manually every frame, while checking for collisions. This code would be placed in Update().

In the second example, the player controls the initial x-axis velocity. This looks as if the player is throwing an object and forgetting about it, vs how the previous one IS the object. This would be placed in an initialization method, such as Throw().

The main difference between these two methods is if you want to use physics or not. The answer to that question really depends on the kind of game you're making.