We can redefine the bibhyperref format (which produces the linked bits of the citation) to prefer linking to DOIs, URLs eprints etc.
\DeclareFieldFormat{bibhyperreforig}{\bibhyperref{#1}}
\DeclareFieldFormat{bibhyperref}{%
\ifhyperref
{\iffieldundef{doi}
{\iffieldundef{eprint}
{\iffieldundef{url}
{\printtext[bibhyperreforig]{#1}}
{\href{\thefield{url}}{#1}}}
{\mkhrefeprint{#1}}}
{\href{http://dx.doi.org/\thefield{doi}}{#1}}}
{\printtext[bibhyperreforig]{#1}}}
Links to eprints are quite tricky, so we need a helper function (which is completely due to Audrey).
\makeatletter
\newrobustcmd*{\mkhrefeprint}[1]{%
\iffieldequalstr{eprinttype}{arxiv}
{\href{http://arxiv.org/\abx@arxivpath/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{hdl}
{\href{http://hdl.handle.net/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{jstor}
{\href{http://www.jstor.org/stable/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{pubmed}
{\href{http://www.ncbi.nlm.nih.gov/pubmed/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{googlebooks}
{\href{http://books.google.com/books?id=\thefield{eprint}}{#1}}
{#1}}}}}}
\makeatother
Now citation links are to DOIs, eprints, URLs or to the bibliography (in that order).
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[backend=biber, style=authoryear-comp, natbib]{biblatex}
\addbibresource{biblatex-examples.bib}
\usepackage[colorlinks, citecolor=red ]{hyperref}
\DeclareFieldFormat{bibhyperreforig}{\bibhyperref{#1}}
\DeclareFieldFormat{bibhyperref}{%
\ifhyperref
{\iffieldundef{doi}
{\iffieldundef{eprint}
{\iffieldundef{url}
{\printtext[bibhyperreforig]{#1}}
{\href{\thefield{url}}{#1}}}
{\mkhrefeprint{#1}}}
{\href{http://dx.doi.org/\thefield{doi}}{#1}}}
{\printtext[bibhyperreforig]{#1}}}
\makeatletter
\newrobustcmd*{\mkhrefeprint}[1]{%
\iffieldequalstr{eprinttype}{arxiv}
{\href{http://arxiv.org/\abx@arxivpath/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{hdl}
{\href{http://hdl.handle.net/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{jstor}
{\href{http://www.jstor.org/stable/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{pubmed}
{\href{http://www.ncbi.nlm.nih.gov/pubmed/\thefield{eprint}}{#1}}
{\iffieldequalstr{eprinttype}{googlebooks}
{\href{http://books.google.com/books?id=\thefield{eprint}}{#1}}
{#1}}}}}}
\makeatother
\begin{document}
\citep{kastenholz,cicero,baez/article,ctan}
\printbibliography
\end{document}
