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You can perform a trick called a Change Level Delay, where you can move near freely through a level change and appear there on the next map. In Old Engine the command 'wait' works differently to how it does in New Engine.
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Propclimbing/propflying is another feature in Old Engine, Since Valve didn't really program what happens when a prop is underneath you, you can hold a prop underneath you and repeatedly jump on it to gain speed. I believe speed gain per hop is linear, and can be quite slow to reach the movement cap. The primary method of movement in Old Engine is bunny hopping, holding w and jumping repeatedly.
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There are a far larger set of differences than that.
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