Difference between a letter/short article and a full length article?

In my experience, there is no real difference between "full" articles and "short" articles except for length.

Many journals, especially more recent online-only ones, do not bother with this distinction at all. An article is simply as short or as long as the article turns out to be. Even with journals that do make the distinction, it often has little impact of the de facto length of the material once supplementary material is included---all that is affected is the fraction of the published "iceberg" that is "above water" in the main text. The peer review process is generally the same, and the perceived value the same, just simply some are shorter than others.

In terms of visibility and citations, short articles are typically just as visible (as you have noticed). I have never seen a citation attempt to distinguish between short and full articles, and most citation formats have no way that one could do so. For those who are affected by publication statistics (e.g., impact factor), that's not affected either: these are calculated by journal, not by article category within a journal.

In short: some things are just shorter than others, and that has little effect on their significance. The editor thinks your article will work better in "short" than "long" format, so take their offer or risk rejection pointlessly.

From the author's point of view there isn't much difference between short letters and full-length articles, aside from length. Some of the differences not mentioned yet are:

• The journal might group its letters together and its full-length articles together. For example its website might have a "letters" section and an "article" section; its print issues might have the letters first then the articles.
• Some small administrative changes that you'll never notice unless someone points them out to you, for example the article ID might change. One publisher I worked at had this code where articles with ID 20 are letters, ID 30 are reviews, ID 50 are research articles, etc. If I'm not mistaken this also changes the digits in the DOI.
• It's possible the production process is different, with letters being on a fast track since they're shorter and so quicker to process.

These are minor differences though. Since the practical differences are so few I'd just accept the editor-in-chief's suggestion - no reason not to.