Preserving privacy in contemporary NLP models allows us to work with sensitive data, but unfortunately comes at a price. We know that stricter privacy guarantees in differentially-private stochastic gradient descent (DP-SGD) generally degrade model performance. However, previous research on the efficiency of DP-SGD in NLP is inconclusive or even counter-intuitive. In this short paper, we provide an extensive analysis of different privacy preserving strategies on seven downstream datasets in five different ‘typical’ NLP tasks with varying complexity using modern neural models based on BERT and XtremeDistil architectures. We show that unlike standard non-private approaches to solving NLP tasks, where bigger is usually better, privacy-preserving strategies do not exhibit a winning pattern, and each task and privacy regime requires a special treatment to achieve adequate performance.