[VMPhil]

I've only just noticed that the RADIO CITY on the tower isn't the same as the cogwheel logotype - is it the same font but in all caps?

Yes! It's always been like that. And, as far as I can tell, that was never the official logo - the lowercase version was the one always used, in various colour schemes over the years, from 2000 (the same year they moved in to the tower) until the "Your" logo launched in 2015.

I can only think that, as the letters/numbers are on their own individual tiles/blocks, as illustrated if you zoom into the below linked photo, that the lowercase typeface would have looked strange if it was put up that way? Or perhaps wouldn't stand out as much as putting it in capitals?

www.flickr.com 

Incidentally, I'm pretty sure the hoarding at the very top of the tower was installed originally to show a big "Liverpool 08" banner when the city was European Capital of Culture. Hopefully if they do get planning permission to change the sign they'll finally remove it as it's pretty ugly looking without anything on it!