Seems like Roman numerals might be better for something but I can't think of why.
For representing specific values in heavy use, e.g. the values of currencies, Roman numerals would be more efficient (sure, the I and V dollar bills are the same, but X and L each save a character, C and D two each, and M three full zeroes!). You also gain information about the approximate magnitude of a number a shade more quickly, though admittedly suffering in precision for less-accessible examples, using the Roman numeral system. For instance, you know when you read the first character of MCMLXXXIV that it'll be >1000, by the third character you know it's 19-something, unlike 1984 which you have to observe in its entirety to even know the order of magnitude. This seems entirely petty and trivial, but if you allow the extended Roman numerals (adding some number of bars above characters to multiply by M) then this advantage propagates out very effectively until you reach numbers of such a size that scientific notation is required for most people to accurately interpret them in Arabic numerals, and remains relevant even for numbers like 8912345678901234567890 (deliberately chosen for legibility in Arabic numerals but other 22-digit numbers could be misread to the extent that carefully counting the number of digits is required to get within an order of magnitude, whereas a 7-barred M would tell you after counting the 7 bars that you're dealing with something e+21; scientific notation admittedly crushes even this corner case except for in even narrower corners)
In Arkansas, California, Iowa, Kansas, Michigan, New Mexico, New York, North Dakota, Ohio, and Rhode Island, you are prohibited from having a custom license plate "69". However, in these states, "LXIX" is not a prohibited license plate. If I would like to reference the only known number whose square and cube contain all of the digits in its base one and only one time on the license plate of my car, I am unable to do so (by law) using Arabic numerals. For law abiding numerophiles of certain U.S. states, Roman numerals offer utility not found in Arabic numerals, therefore Arabic numerals cannot be considered a pareto improvement.
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