According to the data from the Scopus publication database, as analyzed in several recent studies, more than 70,000 papers have been published in the area of Software Engineering (SE) since late 1960's. According to our recent work, 43% of those papers have received no citations at all. Since citations are the most commonly used metric for measuring research (academic) impact, these figures raise questions (doubts) about the (non-existing) impact of such a large set of papers. It is a reality that typical academic reward systems encourage researchers to publish more papers and do not place a major emphasis on research impact. To shed light on the issue of volume (quantity) versus citation-based impact of SE research papers, we conduct and report in this paper a quantitative bibliometrics assessment in four aspects: (1) quantity versus impact of different paper types (e.g., conference versus journal papers), (2) ratios of uncited (non-impactful) papers, (3) quantity versus impact of papers originating from different countries, and (4) quantity versus impact of papers by each of the top-10 authors (in terms of number of papers). To achieve the above objective, we conducted a quantitative exploratory bibliometrics assessment, comprised of four research questions, to assess quantity versus impact of SE papers with respect to the aspects discussed above. We extracted the data through a systematic, automated and repeatable process from the Scopus paper database, which we also used in two previous papers. Our results show that the distribution of SE publications has a major inequality in terms of impact overall, and also when categorized in terms of the above four aspects. The situation in the SE literature is similar to the other areas of science as studied by previous bibliometrics studies. Also, among our results is the fact that journal articles and conference papers have been cited 12.6 and 3.6 times on average, confirming the expectation that journal articles have more impact, in general, than conference papers. Also, papers originated from English-speaking countries have in general more visibility and impact (and consequently citations) when compared to papers originated from non-English-speaking countries. Our results have implications for improvement of academic reward systems, which nowadays mainly encourage researchers to publish more papers and usually neglect research impact. Also, our results can help researchers in non-English-speaking countries to consider improvements to increase their research impact of their upcoming papers.