There many proponents to teaching differential forms and others teach with tensors. This is true for both mathematics and physics education. It seems mathematicians prefer to teach differential geometry using differential forms. I want to know what is the current trend in theoretical physics, do they prefer to develop theory in terms of differential forms, or in terms of tensors (with indices). It seems most authors report that differential forms become more elegant when dimensions of a manifold increase and they also allow to write down equations without the use of indices.
There are the books, "Modern Classical Physics" by Kip Thorne which uses Tensors, "Gravitation" by Wheeler and Thorne which uses differential forms, "Modern Differential Geometry for Physicists" by Chris Isham which use differential forms, and "Geometry of Physics" by Theodore Frankel which uses differential forms. Judging by Isham, Frankel and Wheeler/Thorne(in Gravitation) who are all extremely respected scientists, it would seem differential forms are the standard tool. But I dont understand why Kip Thorne would go with the differential forms approach in Gravitation and yet stick to Tensors in "Modern Classical Physics". Why didnt Thorne use differential forms in his book "Modern Classical Physics". So I thought there was a trend towards differential forms but then Kip Thorne wrote his book "Modern Classical Physics" in terms of tensors, so now that he won a nobel prize, it certainly seems that Tensors are extremely relevant. I just want to know why not differential forms?
From what I read, differential forms seem to be useful for Gauge Theories but then again gravitation is taught in the language of differential forms in Gravitation.
Is it possible to do modern theoretical physics entirely with the use of differential forms and not resort to any tensors? What are the advantages to this? Are there any other more modern alternatives to using differential forms and tensors?
Hoping you theoretical physicists can help lead me on the right path here! Please comment on the textbooks I mentioned, if they are "Modern" in their use and if they are any good. Which is your favourite textbook for differential geometry for physics and do you have any other recommendations?