I've just recently started developing my own chess engine, so i am by no means an expert. But ill still share my thoughts.
I think you can't make a generalization about search speed, as each search engine utilizes different parameters for its evaluation, resulting in cutoffs in search performance. Additionally, certain engines incorporate extensions when they encounter a "good capture" or early exit conditions.
Most search engines provide an output in terms of nodes per second (nps) for measuring the combined speed of evaluation and search. Nevertheless, it's crucial to understand that the interpretation of this metric may differ across engines, as some may include Transposition Table Lookups and other edge cases in their nps calculation.
Another approach for measuring evaluation speed involves disregarding the search phase and focusing solely on static evaluations performed on predetermined board positions. However, this method can be challenging to interpret as well. This is because some engines employ a complex static evaluation process, which may take longer, while others opt for a simple static evaluation but rely on a complex move-ordering algorithms. Ultimately, it's difficult to determine which approach is more effective and thus difficult to say which is more important.