What type of research is more applicable in modern research?

There are various types of research studies circulating within and beyond the modern academy. For the social and natural sciences these include descriptive research, exploratory research, explanatory research, action research, survey research, cross-sectional research, longitudinal research, experimental research, case studies, pilot studies, ethnographic/field research, meta-analysis and synthesis research, observational research, and causal studies, among others. Common for the humanities are archival research, theoretical research, comparative research, interpretive (semiological, deconstructive, phenomenological) research.

Yet note that these general research types are only one part of thinking through the research process. All research projects also require clearly conceptualized and explicated epistemological frameworks (theoretical paradigms), literature reviews (existing knowledge about the topic), a formulated object of analysis including questions/hypothesis and the types of evidence necessary to answer such questions, methods for gathering said evidence, and tools for analyzing the data collected. 

In terms of which of these types of research are most applicable to modern research, there is no clear cut answer—beyond the explicit presence of all the components (laid out in paragraph above). This is because evaluating applicability should be based on how well your type of research matches your research questions. Explaining how research method A is the best way to answer research question B, and why such question is of intellectual (and other, such as social, environmental, or commercial) significance, is the only standard protocol for determining the applicability of one's research practice in the modern academy.

While there are trends in which quantitative data analyses are becoming more popular, the reasons aren't necessarily due to applicability but rather to funding and career related opportunities. Although one could argue that the sheer proliferation of accessible big data does make particular types of research (e.g. those that engage big data) a quite historically apropos research practice.