this question inspired me to make the printing of the Url and the Eprint field conditional, so that it only prints if there's no Doi field. Any pointers would be appreciated,
If I use the code posted below, I would like it to remove what I've striked out with red here,

\documentclass{article}
\usepackage[backend=bibtex, style=authoryear-comp, natbib=true]{biblatex} %for digital version
\bibliography{\jobname}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{Holland1986,
Author = {Paul W. Holland},
Doi = {10.1080/01621459.1986.10478354},
Eprint = {http://www.tandfonline.com/doi/pdf/10.1080/01621459.1986.10478354},
Journal = {Journal of the American Statistical Association},
Keywords = {Applied_Economics},
Number = {396},
Pages = {945-960},
Title = {Statistics and Causal Inference},
Url = {http://www.tandfonline.com/doi/abs/10.1080/01621459.1986.10478354},
Volume = {81},
Year = {1986}}
@article{Heckman1990,
Author = {James Heckman},
Issn = {00028282},
Journal = {The American Economic Review},
Keywords = {_MSc},
Number = {2},
Pages = {313-318},
Publisher = {American Economic Association},
Title = {Varieties of Selection Bias},
Url = {http://www.jstor.org/stable/2006591},
Volume = {80},
Year = {1990}}
\end{filecontents}
\begin{document}
\citet{Holland1986} and \citet{Heckman1990} went for a swim.
\printbibliography
\end{document}



Eprint = {http://www.tandfonline.com/doi/pdf/10.1080/01621459.1986.10478354},is aneprintfield.eprintis normally used for online repositories such as arXiv, JSTOR, Google Books where the URL can be shortened using some kind of unique identifier. – moewe Apr 04 '18 at 12:48Url = {http://www.jstor.org/stable/2006591},witheprint = {2006591}, eprinttype = {jstor},– moewe Apr 04 '18 at 12:49biblatexdocumentation has a short explanation about what each field does and what it means. The filebiblatex-examples.bibcontains good example usages of many fields. – moewe Apr 05 '18 at 13:58