Functional annotations have the potential to increase power of genome-wide association studies (GWAS) by prioritizing variants according to their biological function, but this potential has not been well studied. We comprehensively evaluated all 1,132 traits in the UK Biobank whose SNP-heritability estimates were given "medium" or "high" labels by Neale’s lab. For each trait, we integrated GWAS summary statistics of close to 8 million common variants (minor allele frequency > 1%) with either their 75 individual functional scores or their meta-scores, using three different data-integration methods. Overall, the number of new genome-wide significant findings after data-integration increases as a trait SNP-heritability estimate increases. However, there is a trade-off between new findings and loss of baseline GWAS findings, resulting in similar total numbers of significant findings between using GWAS alone and integrating GWAS with functional scores, across all 1,132 traits analyzed and all three data-integration methods considered. Our findings suggest that, even with the current biobank-level sample size, more informative functional scores and/or new data-integration methods are needed to further improve power of GWAS of common variants.