Print url only if doi not present

Your MWE uses BibTeX, but if you are willing to switch to Biber (you really should look into it, Biber offers more features and BibTeX is officially considered a legacy backend now), you can use Biber's sourcemap feature.

\documentclass{article}

\usepackage[backend=biber, style=authoryear-comp]{biblatex} 

\DeclareSourcemap{
  \maps[datatype=bibtex]{
    \map[overwrite]{
      \step[fieldsource=doi, final]
      \step[fieldset=url, null]
      \step[fieldset=eprint, null]
    }  
  }
}

\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}
\addbibresource{\jobname.bib}

\textcite{Holland1986} and \textcite{Heckman1990} went for a swim. 
\printbibliography
\end{document}

To conditionally print the URL you could use the following:

\documentclass{article}

\usepackage[backend=bibtex, style=authoryear-comp, natbib=true,url=false]{biblatex} %for digital version 
\bibliography{\jobname}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{Holland1986,
    Author = {Paul W. Holland},
    Doi = {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}

% print url if no doi
\renewbibmacro*{doi+eprint+url}{%
    \printfield{doi}%
    \newunit\newblock%
    \iftoggle{bbx:eprint}{%
        \usebibmacro{eprint}%
    }{}%
    \newunit\newblock%
    \iffieldundef{doi}{%
        \usebibmacro{url+urldate}}%
        {}%
    }

\begin{document}

\citet{Holland1986} and \citet{Heckman1990} went for a swim. 
\printbibliography
\end{document}