How can I help my English Mastiff (and myself!)?

I have two 11 month old Mastiffs. One is very small (well, small for the breed) due to being the runt and the other is about 120 pounds. They have received the same training and the same socialization. But, the large one is does NOT like new things or people, she is nervous when new things or people are introduced, she is jumpy sometimes and almost seems afraid of new things and people. If something is unfamiliar to her, she tries to run. This is an issue considering her size. The other one is totally opposite. Not nervous about anything at all. Is this just a personality difference? We need to take them to the vet for thier check-up next month and I am afraid the big one will not allow the vet to touch her. She has to get used to strange people before she will let them even pet her and even then it has to be on her terms. She is and has never acted this way with any of our family or kids. She is GREAT with us. This is just when exposed to the unfamiliar. Help!