Reviewing the available literature and doing my own initial tests seems to confirm that the results of the MAD method versus those of the classical MVO are a statistical dead heat with MVO perhaps having a slight return edge - possibly due to MAD, which is more sensitive to fat tails, producing slightly more conservative portfolios*. However for moderate to large size portfolios of 300 or more assets the difference in cacluation time is markedly in favour of MAD and other LP methods. ( Mean Gini and Mean CVaR can be similarly formulated with the common link being through the Absolute Lorenz curve and SSD ). There is also some evidence of MAD methods producing better (lower) out-of-sample tracking errors making it well suited for index tracking and replication purposes
The Mean Absolute Deviation (MAD) is related to the Standard Deviation by the formula MAD:SD=SQRT (2/Pi) or 0.7979 for the strictly normal or Gaussian case. The closer the ratio of your MAD to Std Deviation is to 0.7979 the more 'normal' the data is. This means that in the case where your underlying data is actually normal the optimal weights generated by the LP MAD portfolio optimization model will be the same as those generated using the Quadratic Mean Variance model.
The method does tend to produce more concentrated or sparse portfolios due to the upper bound on nonzero assets being T + 2 see Feinstein and Thapa (1993).
Some R code (not mine) for backtesting and comparison available here https://systematicinvestor.wordpress.com/2011/11/01/minimizing-downside-risk/