The same amount of people as did last year. Because it won't necessarily be the exact SAME people, just an equivalent NUMBER of people.

I am a native English speaker and teacher. Neither sentence is correct. First, with countable things, we use "number" instead of "amount." The word "amount" is only used of uncountable quantities or masses. In this sentence, then, we must say "...the same number of people..." Also, the use of "did" after "as" is unclear, since there are two verbs before it in the sentence: "[can] expect" and "[to] come." Therefore, the verb should be clarified after "as": "We can expect the same number of people to come to our festival as came last year." However, this still is not the best construction. It is a bit wordy. And it feels a bit "clunky" (an idiom that means that the words feel somewhat forced or unnatural, even if they may be technically correct). If I were writing this sentence, it might look more like this: "We expect the same turnout for this year's festival as we had last year." Here, the parallel structure is as follows: "[subject verb] ... the same as ... [subject verb]" "We expect ... the same as ... we had." And "turnout" is a noun that means "the number of people coming to an event." There are other parallel structures that would work for this sentence: "We expect the same turnout for this year's festival as last year's. Above, the word "festival" is implied after "last year's" to form the parallel structure: "this year's festival ... as ... last year's [festival]" Here is another: "This year's festival turnout is expected to be the same as last year's." The parallel structure: "this year's turnout ... the same as ... last year's [turnout]."

It's "as". That because the meaning of "as" in this context means comparing things. You are comparing the number of people at the festival from this year to last year.