Variation in language is ubiquitous and often systematically linked to regional, social, and contextual factors. Tokenizers split texts into smaller units and might behave differently for less common linguistic forms. This might affect downstream LLM performance differently on two types of tasks: Tasks where the model should be robust to language variation (e.g., for semantic tasks like NLI, labels do not depend on whether a text uses British or American spelling) and tasks where the model should be sensitive to language variation (e.g., for form-based tasks like authorship verification, labels depend on whether a text uses British or American spelling). We pre-train BERT base models for the popular Byte-Pair Encoding algorithm to investigate how key algorithmic design choices impact downstream models' performances: fitting corpus, pre-tokenizer and vocabulary size. We find that the best tokenizer varies on the two task types -- with the pre-tokenizer having the biggest impact on performance. Further, we introduce a new approach to estimate tokenizer impact on downstream LLM performance, showing significant improvement over techniques like R\'enyi efficiency. We encourage more work on language variation and its relation to tokenizers and thus LLM performance.