I recommend Chris Daly's 2006 paper for a comprehensive answer this question (GUIDELINES FOR ASSESSING THE SUITABILITY OF SPATIAL CLIMATE DATA SETS Int. J. Climatol. 26: 707-721). In part he writes:
"while the interpolation methods used to develop these fine grids are not any more sophisticated than those used to develop the coarse grids of the past, known spatial climate features previously assumed to be unimportant at the 50-km scale are now very important at the 1-km scale"
WorldClim interpolates climate using elevation, but does not consider factors such as radiation, aspect, cold air drainage etc that can have a big effect at fine scales in mountainous terrain. If you ignore these other factors and use WorldClim you will likely predict species moving up and down mountains because elevation is the only factor considered when producing the climate grids. If you use more sophisticated climate grids you can potentially identify microrefugia and more complex responses to climate change.
Sorry, not an answer but an area of interest to me. @Rodney Martinez, do you have a pdf of the article you mentioned? I followed the link but the download links were not working?