For a move from 100 to 105, the simple return is 5.00% and the log return is ln(1.05) = 4.879%. The gap widens fast: a move from 100 to 200 is +100% simple but 69.3% in logs.
Logs are preferred for statistical work because a two-day log return is just the sum of two daily log returns, so aggregation, autocorrelation and volatility scaling all behave. They are also symmetric: down 10% in logs is exactly the reverse of up 10%, whereas a 50% simple loss needs a 100% simple gain to recover.
Use simple-returns when you are computing what actually landed in the account, especially for portfolio aggregation across positions in one period, where simple returns are the ones that add up across holdings.
Related: simple-returns, arithmetic-vs-geometric-return, compounding, volatility