I think Eggy makes a distinction between the two. It's more of a reaction to WHY they came than the actual act of rescuing her. Since Siuan and Gawyn came to save her, against her orders, they're in trouble. She's mad because of the implication that they know better than her and need to do as they wish, instead of as she has ordered.

She lets Bryne off easy on the technicality that he came to keep Siuan safe (and she couldn't be talked out of going). She's still mad at him, just not like the other two.

I think she's wrong there, because IIRC he agreed to come to both protect Siuan AND rescue Egwene. I wouldn't correct her if I were Bryne either!