This may be a little long winded by I'v been doing some research for work on this topic. So here it goes...
Protein levels: Another important distinction between six- and two-row barley cultivars is in the average level of grain protein. A high protein level often indicates a thinner kernel with less starch available for conversion to malt extract. Acceptable six-row malting barleys may range from 12 to 13.5% protein, whereas two-row cultivars range from 11 to 13%; barleys with greater than 13.5% protein are rarely used for malt. The high temperatures and moisture stress frequently encountered in dryland conditions (under which most six-row barley is grown) can limit the amount of grain fill (starch synthesis) and thus result in higher protein contents.
The protein content differential is also related to genetic differences in how each cultivar accumulates protein during grain development. Total protein content is defined as nitrogen content x 6.25. Because the net loss of nitrogen during malting is minimal, the total protein content does not change greatly in the process. Much of the barley protein, however, is converted into a soluble form by proteolytic enzymes; a portion of this is further broken down into amino acids and peptides in the wort.
Six-row malts tend to yield higher levels of wort-soluble protein. The ratio of soluble protein to total protein is an indication of the extent of protein breakdown (modification) during malting: 40-45% is considered acceptable.
Higher protein malting barleys are generally believed to inversely reduce the level of malt extract in the kernel. In addition, high protein content can lengthen steeping time, cause erratic germination (especially if grain traders blend low- and high-protein barleys to meet protein limits), increase malting losses, and increase enzymatic activity and, ultimately, the level of dimethyl sulfide. High soluble protein levels can sometimes result in brewing or beer-quality problems.
Malt enzymes: Six-row malts traditionally (that is, before recent breeding advances) yielded higher levels of the desirable starch-degrading enzymes a-amylases and greater diastatic power (DP). a-amylases are the enzymes that convert starch to dextrins, reduce mash or cooker viscosity, and increase the susceptibility of starch to ß-amylase attack. DP is a measure of the activity of the malt enzymes that break down complex carbohydrates into reducing sugars (principally ß-amylase, the key saccharifying enzyme responsible for converting starch to fermentable maltose and for further breaking down large dextrins). The modern two-row cultivar Harrington, however, has levels of a-amylases equal to or slightly greater than those of current six-row malting cultivars. Despite the recent advances in favor of more a-amylases, two-row malts continue to have considerably lower levels of DP -- a potentially limiting factor in some applications, such as when high levels of unmalted grains are used as adjuncts.
ß-glucans. The ß-glucan content of most barley cultivars falls between 4 and 7% of the total grain weight. In general, the ß-glucan content of six-row barleys is slightly lower than that of two-row barleys. ß-glucans are usually extensively degraded by malt ß-glucanase enzymes during germination, meaning that little will be extracted into wort. Undegraded ß-glucans contribute to viscosity and can cause wort separation and beer filtration problems. Both two- and six-row North American malts tend to be well modified; ß-glucan-related problems are not often encountered but are more likely when undermodified malt or high levels of umalted barley are used.
These two topics are of most interest to home brewers.
There is a lot more but it has to do with economic considerations and production climate. If any one is interested we can start a new thread and discuss further.