Apidra undoubtedly works faster for me by a significant amount. In fact I use it when doing corrections with a syringe. The down side is that in tappers off too rapidly for slow meals. So it requires a dual-wave bolus. Unfortunately it doesn't have good durability in a warm insulin pump. So if I were to use it for pumping, I would use a steel infusion set and a 2-day cycle. I never leave Apidra out of the fridge for more than a minute or two. That way I don't end up throwing it away before the expiry date.
Originally I was always Rx'd Humalog and therefore ended up using it in the pump. But I read that it might cause pump blockages so I tried NovoLog/NovoRapid. I still currently use NovoRapid. For me, it is slightly, but consistently faster acting than Humalog and it is extremely durable in very hot weather.
But I must emphasis that these are just my personal experiences. Some people, because of their immune system get differing performance from various analogs. So I would suggest trying all three.