I wore the 5600C for about 12 years when I was in my teens and early 20's. That watch endured horrors that no watch should have to, and survived them all. It was also worn in the ocean on average of about 4 times a week. I literally do not have enough good things to say about the lasting power, and durability of the 5600C. I just recently picked up a 5600E and wanted to give a very short review on what I see as the strengths and weaknesses between the two watches.
Weight: I wore the 5600C for so long, it was like part of my body. The first thing that struck me when I got the 5600E was the weight of course. It is very noticeably lighter, and feels cheaper. This actually almost dissuaded me from buying the E, but I ended up taking the plunge anyway, and am very glad I did. Although my intuition tells me the C is probably a stronger and more durable watch, I have quickly changed my opinion on the E's relative lack of robustness. Within the first day I noticed how nice it is to have such a light watch on the wrist. Only time will tell the real truth as far as I am concerned, but I am convinced at this point that the move toward a lighter make was a wise one. If you know anything about Newton's second law, a light object will have less of a force upon impact, all things being equal, than a heavy one. In essence, this lighter make E may have potential to be more shock proof than it's older brother. If I had to guess, i'd say the gains made in the weight were offset by sheer quality of the C however. All in all, after thinking about it some, the lighter make seems to be a very practical design decision.
Backlight: The first thing I noticed was the backlight. Although i'm sure many watch buyers love the bright blue backlight, this is actually the weakest "improvement" as far as I am concerned. It obviously uses a ton more battery. It is also just too dang bright. When do we need to use a backlight? When it is almost completely dark, or pitch black, right? I just don't think it needs to be that bright, and i'm sure people in say the military would feel the same. All that said however, it does look kinda cool and i'm sure this feature has sold a lot of watches, which no doubt was Casio's intent. Can't hold it against them for needing to make a buck. I am just tickled to death they are still producing this watch is the truth.
Alarm/Timer/Stopwatch: most of these were welcomed improvements. The alarm has been much improved by enabling the user to set an alarm for a specific date, a specific month (ie every day that month), or even a specific day of each month. The old C model gave no allowance for a month/day input. Timer was also improved. It has been a while since I had my old C, but I am almost certain you could not execute a timer under 1 minute. The new E model allows you to execute timers under 1 minute, in 1 second intervals. Very nice. There is also a repeat timer function, where the timer starts again once the time is up. This could be very useful of course. The stopwatch is effectively the same. There may be the ability to do something more on the new E, but if so I could not tell. Truth is, I hardly ever used the stopwatch on my C, I used the timer and alarm a lot however.
"Backlight function": This function triggers the battery draining EL light when the timer, alarm or hourly beeps sound. I can see this being useful in certain instances. If you feel you may be in a noisy environment like a bar or club when your alarm goes off, or perhaps if you wanted to use an alarm for scuba. The truth is however, I feel this is a somewhat useless "improvement", it is nice you can disable it.
In short, my overall review of this watch, and its improvements is that they have done a really amazing job of keeping the simplicity there, while lightening the watch and perhaps going overboard in an instance or two. I'd have to say the new E is more comfortable, and the overall functionability of the watch has improved. The watch has been keeping GREAT time, and I highly recommend it to anybody, but I doubt it even needs my recommendation. This watch obviously spurred on the entire and successful G-shock arm of Casio. If you want a no nonsense watch, for a great price, you needn't look further, that is for sure.