I'm a 3rd-year Linguistics undergrad and this textbook was used in my Syntax class this semester. I have no previous experience with syntax except about a week's worth of overview in Intro to Linguistics. I have read 20 of 28 units in Grammar as Science and I find it frustrating and misleading. I read about 20 pages in An Introduction to Language, which explained a lot of the material in a clear, straightforward way that I understood in one night. I am not familiar with any beginning syntax textbooks, but I'm assuming there's a better one than Grammar as Science.
The text is structured in such a way that is intended to make it easier, by simplifying many aspects of grammar, introducing them in one way at the beginning, and then eventually showing you how it's actually done. The simplified explanations are wrong, but presented at first as if they were right. This was really confusing for me. I wasted a lot of time trying to figure out why it didn't make sense, when really I should have just read ahead to discover that it didn't make sense because it was wrong. I can't speak for everyone, but I would have found it much easier and less stressful to be taught the unsimplified version from the start. Even if it's more complicated, that doesn't mean it's more difficult to understand.
I also found the style off-putting. There are cartoons with speech bubbles that contain text that doesn't make sense as dialogue. The Intro is a strange metaphor relating the textbook/the study of syntax to an adventure, referring to "terrain", "maps", and "guides", complete with a cartoon of Noam Chomsky with a safari hat on. This is pretty insignificant and probably doesn't bother most people, but I found it kind of patronizing and it's a good example of the un-straightforwardness (for lack of a better word) that dominates throughout the book.