WieWaldi The Casiotone CT-S1 piano sounds way better than either the e373 or e383, and the keyboard has a better feel. If one was wanting rhythm accompaniment, the Casio choice in that price range is the CTX700, but the keyboard is rather noisy, from some reviews I've read.
In the US, the e373 and e383 are, $179 and $199. If having more bass from the speakers, without messing with the EQ, is important, then the e373 is a better choice. The e383 speaker output is more of a flat response, similar to studio monitors, or monitor headphones, but can be adjusted with the onboard EQ to suit the player's taste, or lack thereof. Personally, if I were buying a keyboard of this type, I don't think I'd use the speakers very much.
For $20 more, i think the added instruments (particularly the extra pianos) and rhythms, along with the new, easier to use, interface is worth it. The e383 also has the new "articulation" feature.
However, both the e373 and the e383 have the known issue where the sustain pedal does not register in some DAW programs, including GarageBand, unless one makes a workaround by using the split keyboard feature, then registering the split ranges to zero on both sides, then saving the setting as a user registration. A minor drawback in either case of two nice little keyboards.
Anyone interested in the Casio CT-S1 or Yamaha PSR E373, E383, would benefit from looking at Masataka Kono's videos playing these keyboards. He really likes the CT-S1 and plays the heck out it, showing what it is capable of. If not for the rhythms, I'd probably get the CT-S1.