The Scoville unit was developed by American chemist Wilbur Scoville in 1912 to rank the hotness of peppers. The test is organoleptic and is a limit of detection type sensory method using dilution. This is basically a process where the test sample is diluted and the dilutions are tasted until no perceptible “hotness” is detected. The limit of detection is a known (I don’t know this number) and the undiluted level is calculated by multiplying the limit of detection by the dilution factor in the test. Like many sensory methods used to assign quantitative results this method has the problem of using human judges. Not all judges have the same perception and there is another phenomenon in this type of sensory study known as response bias that leads some judges to delay indicating their perception of a stimulus until it becomes obviously present. So there are difficulties with these types of methods. Modern methods for pepper hotness use liquid chromatographic columns to separate various compounds found in peppers and a detector to quantify the amounts of the various components that are separated by the column. This method allows for the quantification of capsaicin; the stuff the makes peppers hot.
The measurement of bitterness in beer is similar to the direct measurement of capsaicin in peppers, except the compounds being measured are different. The bench top analytical method used for years to measure hop bittering compounds in beer involves solvent extraction of these compounds using isooctane and then measuring absorption of ultraviolet light at 275 nm by the solution (this method published by the American Society of Brewing Chemists is more involved than this description, but the details of the method are not critical for this discussion). After crunching numbers using a simple formula you obtain the result of the test and the units are presented as International Bitterness Units. Supposedly one IBU is equivalent to 1 mg of iso-alpha acid per liter of beer. The problem with this is that there is a wide range of iso-alpha acids found in beer so this method is not a direct measurement of any one specific compound.
Over the last twenty years or so high performance liquid chromatography (HPLC) has become more common for the analysis of beer. As with the measurement of capsaicin it is quite common to directly analyze for the various components of beer, including specific iso-alpha acids. While an HPLC is not a cheap analytical tool, it is very useful for a wide range of analytical uses. HPLCs (and gas chromatographs) are now common in medium and larger breweries.
Whether using the older UV spectrophotometer method or HPLC techniques, there is still the complication that IBUs do not really correlate with perceived bitterness because other aspects of beer affect the perception of bitterness. For example, two beers containing 25 IBUs will be perceived very different with respect to bitterness if one beer had an O.G. of 10 °Plato and finished at 1.5 °Plato and the other beer had an O.G. of 12.5 °Plato and finished at 2.5 °Plato. Begin varying the malt bill by adding crystal malt, for example, and changing the content of various water salts and things become even muddier. This is the reason that measures like the IBU are extremely useful when used within a population of similar beers, but not so handy when looking at very different populations.
The alpha acid unit really has nothing to do with IBUs and certainly does not resemble a Scoville unit. Some large brewers have hop schedules that are based on pounds of alpha. This is a handy measure because it is easy to vary the hop bill as alpha varies from bale to bale. Ten pounds of hops with 10% alpha represent 1 pound of alpha just as 20 pounds of hops at 5% alpha do. The alpha acid unit is a bit different; if you add 10 AAUs to a batch of beer using 10% alpha hops you add 1 ounce. The caveat is that the AAU is specific to a 5-gallon (19 L) batch. The same 10 AAUs could be added by using 2 ounces (57 g) of 5% alpha hops to a 5-gallon (19-L) batch.
I personally do not like the AAU because it is pegged to the 5-gallon (19-L) batch. I suppose it doesn’t have to be since it is really just the ounce equivalent of pounds alpha, but it often is assumed that the batch size is 5 gallons (19 L). When most homebrewers were brewing 5-gallon (19-L) batches this measure was handy to many, but some homebrewers today are brewing smaller batches and many others are brewing larger batches. I think this is why the IBU has become much more common, since the IBU calculation includes the batch size as part of the equation and 20 IBUs is 20 IBUs, whether you are brewing 5 gallons (19 L) or 25,000 gallons (94,635 L) per batch (common size for many of the largest US breweries).