Your Big Bully was probably burning up in the heads and was either hitting flat or leaving ringing tens. Really doesn't matter though, the Raging gave you more length and you probably had a sharper angle into the pocket. More energy stored and unleashed at the pins instead of in the heads and mid lane. Sounds like you made a good move, bet you wish you made it sooner.
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As with all things, this is my opinion. And we all know, opinions are like butt-holes, we all have one.