As all three tools are packet sniffers, I would have expected them to give me the same results when I use them to monitor my home's network, but they don't. Therefore what are the core differences and which one is the best to use?
closed as off-topic by RoraΖ, Steve, Steffen Ullrich, schroeder♦ Sep 27 '17 at 16:35
This question appears to be off-topic. The users who voted to close gave this specific reason:
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Airdump-ng is for capturing 802.11 frames, so you use this tool exclusively for wireless networks.
Wireshark and TCPdump are similar but Wireshark is more complex, also has a GUI. E.g. you can set many filters and perform more advanced analysis. TCPdump is more lightweight.
Which one is best to use is a broad question and is up to you, depending on what you need. You don't have to limit yourself to one if you think you need several different sniffers.