which metric is better for boosting methods
Depends.

The first thing that has to be clear is that you are running an experiment, which means you need to measure both with the same metric.

Which one? Depends on which underlying problem you are solving, if what you are doing is to determine which algorithm is better, your conclusion will only be applicable to your specific dataset


Accuracy: Is possible to measure the accuracy as the comparing metric, but it becomes trivial if your dataset is unbalanced, which means you have much more positives than negatives or viceversa. The accuracy is used when the dataset is balanced and if is equally bad to have a mistake on positives and negatives. Also, it has the problem of being too dependant on the threshold for defining positives/negatives.
Area Under the Curve: The AUC is one of the most robust metrics for measuring the ability of a model to separate positives and negatives, is unsensitive to threshold and immune to unbalanceness. I would use this.
RMSE: I only know RMSE for continuous regression, not for classification.
LogLoss: Its use is in multinomial classification