What is meant by imperfect sage mode? I thought Jiraiya had a partial toad-like appearance because he fused with Fukasaku and Shima. And the more nature chakra one absorbs the more characteristics will be visible, except for Jugo's clan that is.
Remember Naruto when training for senjutsu was transforming into toad because he absorbed more nature energy than he can handle. That is how he defeated Preta path (because he kept on absorbing nature energy more than required and Preta path absorbed from him).
So if the degree of sage mode is given based on strength, then Nagato never wanted to kill Naruto but only capture him (that is why he sacrificed Human path). On the other hand Nagato wanted to kill Jiraiya because he could hinder Akatsuki's plans.
And also Jiraiya returned to his original appearance when fused only with Fukasaku. So isn't Jiraiya actually an adept in sage mode because he can absorb more nature energy without turning into a toad stone?
(Of course now Naruto's sage mode is at top considering six paths power in him)