i am not sure what is better i personally believe that one can take something he himself said as it is is his personal honor but an institution like beis din should not because this is not personal honor it is rather the kovod of torah
there is a case in Gittin were Rav(or rebbi im not so sure) and his B”D made the wrong valuation of a terrain, the mistake was more than 1/6 of the price, rav (rebbi still not sure) paskened that the object had to be taken back when asked if he didn’t hold like RSHBA”G that “ma koach B”D iaphe” what would people say about the power of beis din he said beis din should not take it back so that people remain honoring its rulings. notice how he took back what he previously said of taking back (gittin fourth perek i believe lamed daled amud beis but not so sure)