Main factors in deciding between whether to hedge or not: returns, volatility, and correlation. Very briefly:
- Cost of hedge: interest rate differential + any FX basis
- Volatility or underlying vs currency: check if a hedged position can give a better Sharpe; sometimes the currency is more volatile than the underlying
- Correlation between underlying and currency: some assets are better left unhedged i.e. JPY-denominated equities; denomination has a tendency to rise in times of equity stress
Typically, bonds are hedged while equities are left unhedged, but this 'typical' does not apply to everyone at every time - you have to see if it applies to your case.
Also, always do the analysis with your home currency in mind.