word choice - Should I use "and anyway" or "and by the way" in the following case?

It's very unlikely for a planet to hit the Earth. And anyway, why is
he so sure about it? He's not an astronomer."

It's very unlikely for a planet to hit the Earth. And by the way, why
is he so sure about it? He's not an astronomer."

"And by the way, why is he..." has more results in Google Books than "and anyway, why is he..." Not sure if I should trust those figures though.

Answer

Should I use apple or pear in the sentence I love to drink apple / pear juice?

The answer is: it depends entirely on what message you want to convey.

By the way and anyway do not mean the same in that sentence:

It's very unlikely for a planet to hit the Earth. And anyway, why is he so sure about it? He's not an astronomer.

This version could roughly be rewritten as:

It's very unlikely for a planet to hit the Earth. And even if that was not so unlikely, there is another, maybe even more compelling argument: why is he so sure about it? He's not an astronomer.

Whereas the version with by the way would mean something like:

It's very unlikely for a planet to hit the Earth. And oh, yeah, there is another argument as well, let's mention that too: why is he so sure about it? He's not an astronomer.

Although the two expressions are sometimes used to indicate (more or less) the same meaning, I feel that anyway is stronger in introducing a compelling option, one that makes the previous point moot:

You say yes, I say no, but anyway, it's not our decision to make.

The fact that I say yes and you say no doesn't really matter.