Webmail vs Open Source Email Client (like Thunderbird)

Hey, in advance I want to apologize because this is probably a common question, but I haven't found a recent post and neither good information regarding this topic.

Are there any major drawbacks / security / privacy issues when using a Email Client such as Thunderbird, compared to using Webmail. I dont mean being spyed on by the client itself, but rather maybe other programs reading the Emails or something?

Or is webmail even less secure because of web tracking? …

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