Do you guys think a letter (like Vine, tumblr, Facebook, Vimeo) is a better representation of a brand/app than an icon (like SnapChat, Evernote, Twitter, Dropbox)?
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I think depends on strength of a brand.
Icons - images are much more recognizable for eye because they are complex. But thats just visuality.
I don't think just letters are good representation a especially if its a small brand. There is only finite number of letters and their shapes. But for big brands i think it works because... well they are everywhere so you have no problem to remember and recognise them. The simplicity makes them more grand somehow.
Also note, the brands that use just letters almost aways connect strong color with very specific typeface (Klavika that Facebook uses for example).
I don't think its so simple though. Branding can be pretty complicated.
Btw there is great free resource (course) on branding from Wolff Olins - Secred Power of Brands
Icon is better, that letter like "F" (in facebook) is a icon, mind sees as a image