Is the transverse strength of an aligned fiber composite very low compared to the longitudinal strength?

Yes. The transverse strength of an aligned fiber composite is very low compared to the longitudinal strength. This can be understood easily by considering that a pull in the longitudinal direction will be resisted by the fiber, which is normally very much more strong than the surrounding matrix. (To consider an analogy, think of a number of strings of different strengths held parallel to each other - A pull on these will be shared by each string, the stronger ones taking up the larger part of the load). To understand how a pull in the transverse direction is supported, consider a chain consisting of a large number of links that is being pulled. The pull is tranferred from one link to the next and so on. If any one of the links in the chain is weak of damaged, that will be the first to fail and will hence determine the strength of the chain (A chain is as strong as its weakest link). In the same manner, a pull in the transverse direction of an aligned composite will be transmitted repeatedly between fiber width and matrix and the interface between them. Thus the strength in the transverse direction will depend on which of the three (fiber, matrix, interface) will fail first. Since the matrix strength is normally very small as compared to the fiber, the transverse strength of the unidirectional fiber composite is low compared to the longitudinal strength. By the way, if the fiber fraction is very very small, it is possible that the strength is nearly equal in both directions.