I have been told that the English Standard Version (ESV) is the preferred Bible for Calvinists and has a Calvinist slant to it. Is the ESV a better choice than the New King James Version (NKJV)?

I find little merit to the claim that the ESV has a Calvinist slant; it is a balanced translation, although the notes may favor Calvinist theology. But even they are balanced with qualifiers.

Both the ESV and the NKJV are good; the ESV is also high prose, but it is clearer to the modern reader. The NKJV, in my opinion, was not a committee work; it only had revision editors and then was edited by senior editors. The ESV was much more thoroughly debated and uses a little better underlying New Testament Greek text. The NKJV was purposely almost never to differ from the King James Version in semantic meaning. This would make it a weaker translation, since so much scholarship has come about in the last 400 years.