Finding the best way of adapting pre-trained language models to a task is a big challenge in current NLP. Just like the previous generation of task-tuned models (TT), models that are adapted to tasks via in-context-learning (ICL) are robust in some setups but not in others. Here, we present a detailed analysis of which design choices cause instabilities and inconsistencies in LLM predictions. First, we show how spurious correlations between input distributions and labels -- a known issue in TT models -- form only a minor problem for prompted models. Then, we engage in a systematic, holistic evaluation of different factors that have been found to influence predictions in a prompting setup. We test all possible combinations of a range of factors on both vanilla and instruction-tuned (IT) LLMs of different scale and statistically analyse the results to show which factors are the most influential, interactive or stable. Our results show which factors can be used without precautions and which should be avoided or handled with care in most settings.