I find Brighid lovely but that might just be because Brighida was a name I heard a lot growing up and I always liked it. Bridget just makes me think of boring, extremely white (English or fourth generation Australian or something), middle middle class people. Basically Bridget jones-every Bridget I have ever known has been a variation on that theme.
Brigid is marginally nicer. If you have to. I can assure you that people will definitely notice it rhymes with frigid, rhymes with midget, talk about her assets compared with those of Bardot, and that's without bloody Bridget Jones. You might be able to guess my name.