Why is my daughter acting this way?

I have dogs and kids. I've had some scary looking dogs that required a little patience to introduce to people/kids in the past. The sheer size and looks of certain breeds can be very intimidating to many adults and especially to children. Great Danes and mastiffs 'look' dangerous, in comparison to a 35-45lbs border collie.
Your daughter may simply not feel comfortable around large dogs. Suggestion... next time you visit kneel down to your daughters height level to see what she see's when they greet her. Knowing what she see's will give you literal perspective to her view. Stay there with her behind you to let her know it's ok. If she still doesn't feel comfortable it's ok, don't force her. It is instinctual for self preservation to avoid things that we view may harm us even if there isn't a threat.
Let her take her time to warm up to them. Perhaps a baby gate to separate them from her until she feels they aren't threatening anymore. I wouldn't try to force her to interact with them as that can scare her more and make her feel like you don't trust her feelings. As far as her seeking attention. At 4 years old I doubt it. However if that is the case the more of a big deal you make of it the more energy you give to it.

Because they're huge dogs, bigger than her. Her reaction is very normal self preservation instincts.

Have you brought yourself to the same eye level/height as your daughter? Try it and you will see from her perspective. It’s a scary world down there with little protection.

Dogs can react like that to people too