In the process of dialect levelling, the grammatical system of the dialects (tense, nominal case systems, other complex features) usually stays intact. The dialects undergoing dialect levelling are full-fledged languages at each time of the process. The dialects just converge to each other or to a dachsprache dominating them.
In contrast, a pidgin discards all the original complex grammatical features. A pidgin is not considered a full-fledged language. When native speakers emerge in a group of pidgin-speaking peers, they develop a creole with typical grammatical features different from the original languages from which the pidgin was formed. The creole is a full-fledged language.
To complicate matters: When the creole is influenced by one of the original languages, a process called decreolisation can start which can be described as dialect levelling between the creole and the original language.
Note that in any case, dialect levelling is rarely equal to all dialects involved. Usually, there is one dominant and prestigious dialect (e.g., the dialect of the capital city, or a formal hochsprache like High German or Standard Dutch) that gravitates the dialects to itself and absorbes only a few features from the dialects.