I don't know if it counts as a study, but how about a relevant textbook?
The book Biblical Hebrew for Students of Modern Israeli Hebrew looks like it will help you. It's used in the rabbinic program at Hebrew Union College and probably other places (though I only have first-hand knowledge of HUC). Several non-yeshiva programs I'm aware of start by teaching (or otherwise ensuring that students know) Modern Hebrew and then teach older forms based on that. I don't know what yeshivot do.
There are, as you observed, key differences between modern and biblical Hebrew (and the idea of one "biblical Hebrew" also doesn't stand up to scrutiny). These differences are in both form/grammar and vocabulary.
From the author's preface:
Yet BH and MIH are two different languages -- or at the very least, two substantially different dialects of the same language. MIH is certainly useful for reading the Bible, but no one can understand the Hebrew Bible knowing only MIH. There are significant differences in vocabulary, spelling, verb formation, use of verbal suffixes, and word order.
Some constructs in BH are unknown in MIH, such as the vav conversive (reversing vav), a particular formation that converts a perfect verb to imperfect or vice-versa. (BH doesn't really have "past" and "future" tenses so much as perfect and imperfect aspects -- another key difference.) Without knowing about this often-used construct one would make significant errors, some but not all of which might raise contextual alarms ("that doesn't make sense").
Some constructs are different. MIH tends strongly to subject-verb-object order and (to my understanding) doesn't use the direct-object marker et. BH, on the other hand, is less consistent; it tends to put the verb first with the subject and object following, but sometimes starts with the object. Since the verb construct tells you the number and gender of the subject, subjects are sometimes dropped as redundant, which can lead to ambiguity.
BH and MIH handle participles differently, and also some verb prefixes and suffixes. The book has extensive discussions of this. Some vocabulary is also different. While MIH vocabulary is derived from BH vocabulary, knowing only MIH doesn't always get you back to the core.
BH itself isn't completely uniform either. From the introduction:
The second problem alluded to in the term biblical Hebrew was that it implies that we have a single, unified language. On the contrary, we actually have several dialects that are merged in the Hebrew Bible. These dialects may be distinguished mainly in terms of chronology, geography, and genre.
He goes on to point out that the language changed over the span of a thousand years, particularly through exile when Aramaic had a stronger influence; that there were differences between the northern and southern kingdoms after the split; and that poetry is rather different from prose.
Throughout the book he offers some translation tips, which I quote from to illustrate the types of problems that can arise. (I'm going to sometimes transliterate for ease of composing this answer.)
Do not assume that a word has the same meaning in BH and MIH. Example: Song of Songs 4:1 שַׂעְרֵךְ כְּעֵדֶר הָעִזִּים, שֶׁגָּלְשׁוּ מֵהַר גִּלְעָד. The word galash in MIH means "ski", but here it means "descend".
(You can see how, given a root for "descend" and a need for the concept of downill skiing, the creators of MH might have applied the former to the latter. This isn't a unique example by any means.)
Vowels matter. In particular, be sure to distinguish between verbs and nouns. Example: Psalm 13:6 אָשִׁירָה לַיהוָה, כִּי גָמַל עָלָי. Gamal with a qametz is the noun "camel", but gamal with a patach as here means "deal fairly" or "reward".
I understand from this book that vowel-driven nuances are way more common in BH than they are in MIH.
He also points out issues with different classes of defective verbs, and with verbs that look the same in different binyanim (so you need to apply context).
For much more discussion, see the book.
The book lists the following source that sounds promising; I haven't seen it but I trust Davïd's recommendation:
- Saenz-Badillos, Angel, A History of the Hebrew Language, Cambridge University Press, 1993 (preview on Google Books, h/t Davïd)
Further recommendations from Davïd: