Biopharma Finder is specifically designed for the analysis of biopharmaceuticals, providing features like intact protein analysis and peptide mapping which are important for the analysis of biopharmaceuticals. I am using BF for peptide mapping which is required as part of multi-attribute method (MAM). A colleague is using BF for the analysis of oligonucleotide but I have never done this.
Proteome Discoverer is a more comprehensive software suite that covers a broader range of proteomic data analysis tasks and workflows, including protein identification, quantification (also LFQ), PTM analysis, and protein interaction network analysis.
To get more info I would recommend to download the user manuals for both software to learn about their respective features.