I found help in both the Brown-Driver-Briggs lexicon (BDB) and the New International Diction of Old Testament Theology and Exegesis (a.k.a. NIDOTTE, ed. VanGemeren).
'tawek' appears as a substantive or adjective, meaning "middle" or "center". It most often appears with the 'bet' preposition, 'betok', with an emphasis on "in", as in "in the very midst of", or "in the very heart of". It is used by most writers of the Hebrew Scriptures around 8-10x per book, but most often in the Psalms.
'qereb' has a broader range of related words from the root 'qrb', like the question acknowledges, but 'qereb' refers often to internal organs, and "inner parts". BDB lists the primary definitions as being under numbered and lettered headings, traced here: 1) the inward parts of a human being (or a city, a house, land, number of persons, the hand, or time); 2) inward part of of man (seat of thought or emotion, the faculty of thought; 3) as a technical term for entrails. There are frequent uses of most headings under "1)".
So the difference is that 'qereb' denotes an "inward part" and 'tawek' denotes the very "middle" of something. Therefore we can expect to find quite a few similar uses. However, since the root of 'tawek' does not have any significance in the theology of the Hebrew Scriptures (its root is not used in any other derived forms), and 'qereb' does - if someone were to want to do further exegesis on a particular text, the usage of 'qrb' derivatives may bear significant meanings.
Both 'betok' and 'beqereb' are well attested in a range of uses and the use of one over the other does not appear to me likely to affect the interpretation of any particular passage.