Most of the time backtest results are better using monthly rebalancing. Also quarterly rebalancing is not so good because the lookback period of many strategies is also a lot of times around 3 month. Rebalancing quarterly would result in bigger rebalancing trades. Using monthly rebalancing you do more smaller adjustments. Trading costs will be very similar. Three month is a long time, too long if markets begin to go down. Using QuantTrader you can switch to quarterly rebalancing to check the backtest results.