I would prefer specialized programs like Botany/ Zoology/ Microbiology. Because, these programs at the under graduate level will hep you to understand the basics/ laws of nature, how it functions, etc. when you graduate up from courses like these your fundamental knowledge of science improves and you can think way ahead to improve the way of living. In future you can go for more specialized fields of study/ research. 

Today generation and even company/institute requirement has gone so specialized that general bioscience course has no needs. Even for specialized Microbiology course, people opt for futher specialization like agriculture microbiology/ industrial microbiology/ medical microbiology course.

I believe that graduation in Zoology or  Botany or Microbiology, cover basic required for general bioscience and one can opt for futher specalization in post graduation as per need. In India, most of the graduation cover zoology, botany and microbiology in 1st and 2nd year of graduation course and than in 3rd year you can then select any one specialized course.

A specific and specialized one. 

very good question, i agree with Amarchand Chordia Murugan answer 

Specialized programs like Botany/ Zoology/ Microbiology are in itself diverse e.g. I studied Botany including Plant taxonomy, Plant Morphology, Plant Biochemistry, Phyto geography, Mycology, Phycology, Physiology, Pathology, Anatomy, Genetics,etc.,;and most interrelated the Plant Ecology. 

For complete understanding either way you have to know all related information but do not loose the focus (e.g. botany the plants) and also don't take them away from their environment and climatic interaction. thier interaction with other organisms

Definitely, I will endorse a specialized degree, then only you can able to do full justice to that field.

It all depends on the objectives of the course outlined, level of the course. In my university at bachelor level we can choose inter-discipline (one major two minor) but at masters level only in one discipline (eg botany) with one major (e.g. plant ecology) with few minor from botany. This first gives a broad picture and then paves way to specific field of interest that may lead to specialization. 

Thank you very much for your invaluable comments, as your opinions will help us compare our current degree programs and proposed changes to the global academic community. Following a multitude of leveling-off workshops, my university opted to retain the specialized programs with major and minor options for MSc degrees. However, we opened doors for proposed multi and inter-disciplinary tracts for Biological Sciences (as well as Biology Education), and for coupling with applied biology programs or other non-biological disciplnes via dual or joint degree graduate programs (especially in partnership with other universities)