The excellent Forecasting: Principles and Practice, 3rd Edition has a very lucid and technically complete explanation of this that I would highly recommend. 5.8 Evaluating point forecast accuracy | Forecasting: Principles and Practice (3rd ed)
The distinct advantage of MAPE is the percentage interpretation; this attractive feature is built-in. By contrast, MASE is [S for scaled] compared to a naive or seasonal naive forecast; for each individual forecast, numbers greater than one (in absolute value) imply a worse forecast than the NAIVE/SNAIVE and those less than one (in absolute value) imply a more accurate forecast. We then take the mean of those ratios with the absolute value transformation guaranteeing that each component is non-negative.
It is worth noting that one could derive a percentage for MASE by creating a table based on the frequency of ratios between -1 and 1 [or 0 and 1 post abs()] and it would answer what proportion of the forecasts are better than NAIVE/SNAIVE though sans a metric giving any idea of by how much; the how much, on average in the metric of y, is the exact quantity provided by MASE.