Agreed. Most ministries considers <3 relevant exp as fresh grads roles (ie Asst Mgr) that why i was quite surprised over the different in roles offered.

What stage are you at now? Verbal offer stage for SB and final interview at Ministry? If so you can try telling Ministry that you have an offer and would appreciate if they could get back to you.

I have a friend who told his 2nd interviewers about his having another offer, and they gave him a offer within the same say of the interview.

But if you still at initial interview or shortlisting stage, then go with AM is oso good!