The solution that works perfect for me both for bibtex and biblatex is the combination of sloppypar that @fuenfundachtzig mentioned with the \usepackage[hyphens]{url} that proposed by @Suresh.
The next code is used to be able to use both ways (bibtex and biblatex) to compile your file and works for me in cases of natbibs agsm style and bibers authoryear. Actually you don't have to use both ways and the method will work (I think) anyway if you just keep the code of each case (bibtex or biblatex) [except of the trick of @moewe with the url that solved the problem I had in my post here that will be possibly need to be adjusted according to the bibtex style we will use].
\documentclass{article} \usepackage{filecontents} % \UseBibLaTex is a variable that if is less than 1 the document % will have to compiled with `bibTeX`... else with biber \def\UseBibLaTeX{1} % ``url'' package is used in order to make LaTeX to break the urls % in places like the bibliography combined with the next (upcoming) % command %\usepackage{breakurl} \usepackage[hyphens]{url} \Urlmuskip=0mu plus 1mu minus 5mu \ifnum\UseBibLaTeX>0 \usepackage[backend=biber,style=authoryear]{biblatex} \addbibresource{myBib.bib} \else \usepackage{natbib} \def\harvardurl#1{{\bfseries URL:}\space\url{#1}} \fi \begin{filecontents*}{myBib.bib} @Article{cite1, title={One Article with a url that has to break both in bibtex and biblatex}, author={Someone NotMe and Someother Me}, year={2018}, month={10}, url={http://A-long-URL-that-has-to-break-through-lines-and-biber-has-to-ignore-the-url-command}, doi={http://dx.doi.org/10.1038/nphys1170} } @Article{cite2, title={One Article with another url that has to break both in bibtex and biblatex}, author={Someone NotMe and Myself Me}, year={2017}, month={10}, url={http://AlongUrlThatHasToBreak.ThroughlinesAndBoth.BiberAndBiblatex.HasToAcceptTheCitation.com}, doi={http://dx.doi.org/10.1038/nphys1170} } \end{filecontents*} \title{Double Functionality about Bibliography} \author{Konstantinos Leledakis} \date{October 2018} \begin{document} \maketitle \nocite{*} \ifnum\UseBibLaTeX>0 \begin{sloppypar} \printbibliography \end{sloppypar} \else \bibliographystyle{agsm} \begin{sloppypar} \bibliography{myBib} \end{sloppypar} \fi \end{document}
Output with bibtex:

Output with biblatex (biber):
