Timur apparently styled himself on Genghis and yes, I think he did surpass Genghis certainly for his successes against Indian Muslim rulers and also against Mamelukes and Turks at the time. I don't think Genghis or his sons had such victories against as many highly advanced and civilised enemies as Timur did. Granted, their direction of conquest was different and we can never know how far Genghis' armies would have gone into Europe at the time when Genghis suddenly died, but Timur on paper was undefeated and inflicted defeat on more organised and advanced opponents than Genghis. That's just my opinion but you're welcome to differ.