The Han shooting first comparison seems pretty apt. It's not that consequential in the larger scheme of things, but it alters the characterisation to simplify the morality of the cast. You can feel the tonal change a little bit in the overall presentation too. I interpreted the original bombing mission as more high strung, by people in over their head. In the remake people seem more confident and playful, with their quips and banter. Both changes seem to complement each other though.
Changes were inevitable anyway, and arguably kind of the point of doing a complete remakes. The original had inherent ambiguity due to its low fidelity, lack of voice acting, and pretty iffy localisation. When you modernise it, you're going to have to clarify things and make more and harder creative decisions. We don't have to approve of the changes when all's said and done, but I think that until we see what they do with them and what it all builds towards, we should at the very least be open to them. This is not the original FF7, and that version's not going anywhere. Might as well treat this as its own thing.