Here is how I would go:
\documentclass{book}
\usepackage{hyperref}
\usepackage{refcount}
\usepackage{xstring}
\newcommand\Ref{}
\newcommand\RefNum[1]{%
\StrBehind{\getrefnumber{#1}}{.}[\Ref]
\hyperref[#1]{\Ref}}
\newcommand\ChapNum[1]{%
\StrBefore{\getrefnumber{#1}}{.}[\result]}
\newcommand{\myref}[1]{\ChapNum{#1}%
\ifnum\result=\thechapter \RefNum{#1}\else\ref{#1}\fi}
\begin{document}
\chapter{First}
\begin{figure}
\caption{\label{fig1}Figure chap 1}
\end{figure}
\begin{equation}
x+y=z
\label{eq1}
\end{equation}
\myref{eq1}
\chapter{Second}
\begin{figure}
\caption{\label{fig2}Figure chap 2}
\end{figure}
Here see the Figure \myref{fig1}.
\noindent
Here see the Figure \myref{fig2}.
\noindent
Here for the equation \myref{eq1}
\end{document}
The command \myref
acts as the \ref
command if you are referring to something in another chapter and suppress the chapter number if you are referring to something in the same chapter.