Hi Homelilly. I am one of the people who recommended multivariable calc books to you back in March. I see you have chosen a different one from those we recommended, presumably based on the choice of your instructor. Since we have no first - hand knowledge of the background or ability of the student, we recommended based on quality of material in the books, and stature of the authors.
Your question today is relevant, i.e. which edition of Marsden would be more accessible to the student, but it is one we have less ability to answer. The best way to find out if a book is comfortable for the student is to have the student try it. This may be possible by visiting a university library where old editions of a given book are often available, combined with visiting a bookstore where the latest one is found.
I will try to say something of use however. First of all, what books are you speaking of? I.e. I presume you refer to Vector Calculus, by Marsden and Tromba, and Spivak's Calculus on Manifolds. (In my opinion, Marsden and Tromba is a decent book if not as substantial as those we recommended.)
These two books are very different. I have taught from Spivak to average students at a state college, and from the second edition of Marsden and Tromba to honors high school students at a good private school in Atlanta.
Spivak was far too condensed and difficult for my average college students, assuming far too much background and sophistication, and it (and I) created a pressure environment they mostly found inappropriate; (except for one strong student who found it ideal, having transferred in from Notre Dame, and who gained confidence to transfer back there afterwards).
The honors high school students found Marsden and Tromba quite challenging and abstract, with its treatment and emphasis on n -dimensional linear algebra, which was new to them. Still they were so strong and interested, that it challenged and appealed to (most of) them. One of the strongest among them changed his major from English to math, went on to Yale, and is now a well known professional research mathematician. Another of them went on to second year calc at Harvard as a freshman and (I believe) achieved phi beta kappa status, and later a phd in physics.
I suggest you have your student look at Marsden/Tromba, and maybe also at Analysis on Manifolds, by Munkres, which I have not read, but which looks from its table of contents like an attempt to expand on Spivak, making it likely a good companion. Munkres is a very highly regarded author, considered unusually readable.
As to which edition of Marsden and Tromba to prefer, I have only seen the second edition. But a general remark is that in most cases it does not matter which edition you buy of a textbook. I.e. usually the authors do their best on the first edition. Then if it sells, the publishers try to get them to revise it so it will sell more. This may mean putting in more easy problems, or taking out more difficult topics, or even just making minor changes. Only rarely is a later edition thoroughly rewritten and improved*. Hence in general I tend to recommend the cheapest edition, usually an early one. In this case I found a used copy of Marsden and Tromba online for under $10, maybe 1st edition, and a second edition for under $20.
https://www.abebooks.com/servlet/SearchResults?an=marsden, tromba&cm_sp=SearchF-_-home-_-Results&ref_=search_f_hp&sts=t
*PS: Occasionally a later edition corrects errors from an earlier one. My copy of Spivak, published October 1965, has "addenda", on pages 145-6, containing amplifications of some proofs, that are recommended. As I recall they were missing from my first edition printed in maybe January 1965, so you might avoid that earliest printing of that edition. I just noticed also that his 1968 preface to the 1971 version of his book, at amazon, says he has corrected numerous errors and misprints brought to his attention. So I recommend getting the 1971 or later version of Spivak's Calculus on Manifolds, or any copy containing that 1968 preface (even my "October 1965" one does). Here are used copies of Spivak under $30:
https://www.abebooks.com/servlet/SearchResults?an=Michael spivak&cm_sp=SearchF-_-home-_-Results&ref_=search_f_hp&sts=t&tn=calculus on manifolds
From my reading of reviews on amazon, it looks as if Munkres might be preferred to Spivak for similar content and easier readability. Still there is something nice, from my perspective, about having the material presented succinctly as Spivak does, but maybe not necessarily when first learning it.
good luck.
