Antoine, if you keep it, don't get rid of the old hose! That hose handle design is easier to use than the gray one with the black slider they used in the 80s and 90s. If anything ever happens to the handle on the new one you bought, you can swap the handle over to it, the 3 way switch in the handle is identical on both hose handle styles.
Also, you can repair that split in your hose by putting a heat shrink tubing cuff on it....just put it on and use a hair dryer to shrink it in place. Will seal it right up.