I'm actually going to be starting on my Masters in Engineering Management soon.
The choice for you really depends on what it is you want to do. Because of all the "heavy lifting" you do as an undergrad, the ChE Masters is much more focused. If you know something in particular you'd REALLY like to get into, then doing the ChE route may be better for you. If you aren't sure where'd you like to go from here, then I would suggest either EM or even working a bit to see what you enjoy.
In my case, I graduated with my BS and got into the industry right away. I found that I really enjoy production and industrial settings, so the Engineering Management route is what I chose instead. Getting a ChE Masters really changes nothing for me, so I won't be attempting that.