In this paper, we compare the use of linear versus neural classifiers in a greedy transition system for MWE identification. Both our linear and neural models achieve a new state-of-the-art on the PARSEME 1.1 shared task data sets, comprising 20 languages. Surprisingly, our best model is a simple feed-forward network with one hidden layer, although more sophisticated (recurrent) architectures were tested. The feedback from this study is that tuning a SVM is rather straightforward, whereas tuning our neural system revealed more challenging. Given the number of languages and the variety of linguistic phenomena to handle for the MWE identification task, we have designed an accurate tuning procedure, and we show that hyper-parameters are better selected by using a majority-vote within random search configurations rather than a simple best configuration selection. Although the performance is rather good (better than both the best shared task system and the average of the best per-language results), further work is needed to improve the generalization power, especially on unseen MWEs.