As is the case with so many things, we have to go back to the origins of block scheduling to really understand the logic behind it, and its relevance to the modern student and his classroom.
Back before it was taken for granted that everyone would, given the opportunity, go on to college, high school played the role that college does now, in terms providing unrivalled opportunities to its graduates, and virtually disenfranchising those who fail to graduate. A few generations prior to that, middle school performed that function.
In colleges and high schools nowadays students migrate from one specialized teacher (science, math, English, art, etc.) to another over the course of the day. The intent is to ensure that the students gain a broad-based education that will allow them to be competitive in the modern workplace. The middle schools of 150 years ago were also intended to be the last stop on the way to employment. As such, those middle schools had to have similar characteristics to a high school or university.
Educational change in America always has to overcome a great deal of institutional inertia, and in the particular case of middle school, the appropriate change (from a school for soon-to-be factory workers to a place where young children to learn to read and write) is one that never occured on a wide scale. Although some school systems have tried experimenting with alternately unifying middle schools with high schools or primary schools, neither produced the drastic changes in student performance later on that had been hoped for.
Critical factors in determining the effect that block scheduling will have on your child is the nature of his primary school education, your family environment, and the high school you expect him to go on to. If the rigidity of a block schedule fits the educational philosophy of the educational system you are in, then by all means send your child to a school that has it. On the other hand, the reverse is also true.
Ultimately, however, the sad truth about scheduling of any sort in schools (in fact, this is a fundamental truth about almost everything in schools) is that it has little, if any, effect on student performance. The very best predictors of how a student will do in life are closely tied to socioeconomic background, and not to the quality of education the child receives at any point in his life. When push comes to shove, if you went to college, your children almost certainly will too. And in all likelihood, they’ll do better there than you.