There is a smallish, but interesting, literature on the differences and similarities between the philosophical notion of logical form and the linguistic notion of logical form. Without trying to resolve the question of whether or not they should utimately be identified, I want to make a few comments on Frege's notion of logical form and why it is at least conceptually distinct from the linguistic notion.
In the Grundlagen, Frege stumps for three interrelated theses. The two I wish to focus on are his antipsychologistic thesis and the context principle:
always to seperate sharply the psychological from the logical, the subjective from the objective;
never to ask for the meaning of a word in isolation, but only in the context of a proposition;
Now it is familiar that Frege ultimately settled on issues concerning the publicity of content as the primary justification for his antipsychologicism. Early on, however, Frege was at least as concerned with seperating out what we might think of as the purely semantic or logical content of a sentence from that which is not relevant to the sentences truth and/or inferential capacity. Early and late Frege referred to this extra-logical content as "colouring". Here is a quote from the Begriffsschrift:
My initial step was to attempt to reduce the concept of ordering in a sequence to that of logical consequence, so as to proceed from there to the concept of number. To prevent anything psychological from penetrating unnoticed, I had to bend every effort to keep the chain of inferences free of gaps. In attempting to comply with this requirement in the strictest possible way I found the inadequacy of language to be an obstacle; no matter how unwieldy the expressions I was ready to accept, I was less and less able, as the relations became more and more complex, to attain the precision that my purpose required. This deficiency led me to the idea of the present conceptual notation. Its first purpose, therefore, is to provide us with the most reliable test of the validity of a chain of inferences and to point out every presupposition that tries to sneak in unnoticed, so that its origin can be investigated.This component of Frege's thought is not so much a negative concern with psychologicism, as a positive concern with carving out a privileged chunk of natural language meaning. Call this theses semanticism.
Frege makes clear in some of his unpublished work that the tendency of natural languages to obscure the semantic/logical content of sentences motivates his context principle:
What is distinctive about my conception of logic is that I begin by giving pride of place to the content of the word ‘true’, and then immediately go on to introduce a thought as that to which the question ‘Is it true?’ is in principle applicable. So I do not begin with concepts and put them together to form a thought or judgment; I come by the parts of a thought by analyzing the thought” [Notes for Ludwig Darmstædter].The resulting pair of theses (i.e., semanticism and the context principle) essentially define the Fregean notion of logical form, and this is a notion which is patently independent of syntactic structure. Specifically, according to Frege a number of syntactically distinct sentences can express exactly the same semantic/logical content (ultimately, the same thought or proposition). We thus have a grasp of that content which is independent of the syntactic structure of the sentences which express it. And it is in virtue of this independent grasp of the proposition expressed that we are able to generate a logical analysis of the proposition. The resulting analysis is the Fregean logical form.
But notice that, since Frege is explicit that syntactically distinct sentences can express the same proposition, it follows that Fregean logical form can mirror at most the syntactic structure of one of those sentences. Thus, Frege's notion of logical form is conceptually distinct from the linguistic notion of logical form. Of course, Frege was not thinking here in terms of a level of syntactic "deep structure". So he may well be wrong that the sentences he takes to have distinct linguistic logical forms do, in fact, have distinct linguistic logical forms. But the point is that the indentification of the two types of logical forms is an independent philosophical-cum-linguistic thesis that requires independent justification.