More obvious than the difference is the similarity: both sentences are so awkward that it's difficult to understand what they mean.
In both sentences, the subject is "we," the verb is "were," and the complement of "were" is "here."
Then there is the prepositional phrase describing the purpose with the preposition "for" and an object of that preposition, which is the noun phrase "a search of what...."
The noun phrase contains a prepositional phrase describing the search, the preposition being "of" and the object of the preposition being a relative clause. I assume that the identity of the "first sentence" is clear in context, but here it is not. In any event, he relative clause is the difference between the sentences:
what the first sentence was in comparison with
This is a more passive construction. It denotes something that some first sentence was presumably compared to by someone, but it leaves me wondering why the writer didn't use the actual passive voice, namely "what the first sentence was compared to." As it is, this clause describes a state of comparison without even implying that there was any act of comparison.
what we were comparing the first sentence to
This clause is in active voice, therefore more specific, indicating that some group, including the speaker, had compared the first sentence to something, and denoting that thing as the object of the preposition.
Another problem with these sentences is that the proposition of, when used with search, as in a search of something, typically denotes the domain of the search, not the thing being sought. For example, "I couldn't find my gloves despite a thorough search of the closet." But the fact that the object of "of" here is an unknown thing implies that it's the thing you're looking for, not the thing you're searching. To describe the thing being sought, the usual preposition is "for," as in "I searched the closet thoroughly for my gloves."
A related problem is that of the earlier comparison. It's difficult to imagine comparing a sentence to anything other than another sentence or another passage of text of a similar length. It is also difficult to image having to search for that bit of text (did you forget what it was) or to search the text for something else. Perhaps this is clearer in context, but here these sentences are just confusing.
Possible improvements:
- You probably don't want "for" twice in rapid succession as in "we were here for a search for that thing," so you can say "we were here to search for that thing."
- instead of the relative pronoun "what," a noun might be better (this is usually the case). It's more specific. Consider: "we were here for a search of the poem that we compared the first sentence to" or "we were here to search for the famous quotation that we compared the first sentence to but nobody could remember exactly."
