Is there any difference in sense between:

"Which do you use more often, bus or train?"
"Which do you use the most often, bus or train?"

And I guess the article can be left out, right?

Which do you use most often?
KooyeenAnd I guess the article can be left out, right?

Which do you use most often?

Yes. The article certainly can be left out.

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Technically, the first asks you to compare only the two named things, while the second asks you to compare more than two things, of which only the two named are expected as the answer (i.e. expected to be the most used).

In practice, the second is commonly used in the first sense, and most people neither notice nor care. Even so, if you are comparing only the two named things then I recommend the first version as superior.
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Technically, "the" is required by basic grammar rule as "most" is the superlative form. But we often see contexts omitting it. Time modifiers such as "often", or "frequent" should be used along with " the most" in a superlative context.

Compare the following:

1) If you go on to the national lottery website, it will tell you the most frequently drawn numbers. 2) What lottery numbers come up most often?, Notice "the" is missing in the latter sentence.
More often or most often which is correct