This paper presents an analysis and comparison of distinct approaches for data-driven combustion parameter estimation for Diesel engines. Thereby, characteristic quantities are modelled by a set of selected regression models and via a convolutional neural network (CNN). While the former use settings from the Engine Control Unit (ECU) as input, the latter works by processing the raw crankshaft vibration signal. The central point of this study is a broad evaluation of data-driven modelling for Diesel combustion. This includes whether using a signal recorded from individual combustion cycles achieves better representation of the target values than using operational parameters from the ECU which cannot reflect unforeseeable, stochastic phenomena within the combustion chamber. This was evaluated by assessing predictions of six combustion characteristics: the crank angle of 10, 50 and 90 percent mass fraction burned, Peak-Firing-Pressure, Combustion Duration, and Ignition Delay. In two series of experiments, it is established that individual cycle data processed via a CNN does not provide an advantage over feature-based machine learning using operation parameters. Specifically, Support Vector Regression (SVR) and Partial Least Squares (PLS) are found to produce estimates of satisfactory quality when making predictions over varied conditions within a single operating point or extrapolating to an entirely unseen operating point. The results suggest that, at least in selected, practically relevant settings, computationally efficient, classical regression models with low-dimensional inputs can compete with or even outperform neural models trained on large amounts of high-dimensional data. This is underlined by the PLS model outperforming the CNN by an average RMSE margin of 1.99°CA for CA50, and 9.93 bar for Peak-Firing-Pressure, respectively, across all experiments.