Generally speaking, so long as you don't use browser specific properties and such, there shouldn't be a difference in the tests. If you do end up needing to do so, you should put conditional code in to check "If browser is Chrome then bar, else foo"
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Why automate? I do automated testing because there's only so much a human being can do and remain healthy. Sleep is a requirement. So, while people sleep, automation that I create does what I've described above in order to make sure that nothing gets past the final defense of the testing group.
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In addition to Robert's reply, https://support.smartbear.com/testcomplete/docs/app-testing/web/general/cross-browser/index.html help section might help.
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