Permit me to disagree; I think it is useful to internalize the general rule that for every 100x increase in data size the theoretical performance will drop by 10x. This isn't a perfect rule but it is just as valid a shortcut as saying hash lookups are O(1).

For all intents and purposes all modern CPU hardware works the same way (a cache hierarchy, superscalar, pipelined, with relatively slow DRAM hanging off some bus).

In practice measure different approaches to performance-critical code with realistic datasets and don't make assumptions. Don't assume that you know dictionaries are O(1) and therefore searching an array must be slower.