I am looking for a recent comparison of variant effect prediction tools.

There is this older paper from 2013/2014 that argues that choice of transcript data set and variant effect prediction tool has a large effect on variant effect annotation.

Choice of transcripts and software has a large effect on variant annotation http://genomemedicine.biomedcentral.com/articles/10.1186/gm543

I am guessing that choice of transcript data set still makes a large difference (kind of obvious) but I am hoping that choice of variant effect prediction tool makes less of a difference nowadays.

The SnpEff web page mentions that there was an effort to do some standardizatons among variant effect predictors to make them more comparable:

This new format specification has been created by the developers of the most widely used variant annotation programs (SnpEff, ANNOVAR and ENSEMBL's VEP) and attempts to:

provide a common framework for variant annotation,
make pipeline development easier,
facilitate benchmarking, and
improve some known problems in variant annotations.
  

http://snpeff.sourceforge.net/VCFannotationformat_v1.0.pdf

Did this really improve the concordance between different variant effect predictions software (especially SnpEff v.s. Ensembl VEP)?