I think the difference between OTB and online is often exaggerated. If you get better at spotting tactics online, you'll be better at it OTB and vice versa. I do not think either format has a significant advantage when it comes to pattern recognition and calculation.
Having said that, doing puzzles online is more efficient because you do not have to set up the board for each new puzzle.
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If I do puzzles on a real board does that help more even for online chess than just cracking out puzzles on lichess