In my current role as a Data Scientist, I have had the opportunity to work extensively with both Random Forest and Gradient Boosting Machines (GBM). These are both ensemble algorithms which aggregate the predictions of many base models to improve overall performance. The fundamental difference lies in the mechanics of these models. Random Forest builds a multitude of decision trees and merges them together to get a more accurate and stable prediction. Contrarily, GBM builds new trees sequentially to correct errors from previous trees.
I've used these machine learning techniques in different projects. For an e-commerce project where we were developing a recommendation system, we used Random Forest due to its strength in handling a wide range of data with minimal pre-processing and its ability to prevent overfitting. Whereas for a marketing campaign optimization project, we used GBM. In this case, even though it took longer to optimize the hyperparameters, it outperformed the other techniques in terms of the model's precision and recall.