Well, here is a full list of all improvements, from what I can tell:
- 40mm display is 35% larger than 38mm, 44mm display is 32% larger than 42mm
- 1GB RAM vs 768MB for better multitasking
- First 64-bit processor in an Apple Watch with twice the performance for better future proofing
- Two new infographic watch faces for more information at a glance
- The fire/water/liquid metal faces look better, IMO, on Series 4 because they go edge to edge
- 50% louder speaker
- Microphone moved to the right for better call quality
- Built-in ECG (coming soon after final FDA approval)
- Now notifies you of abnormally low heart rates and atrial fibrillation, potentially warning you of an impending heart attack or other cardiological problems
- The new crown is a lot smoother in rotation and has haptic feedback. It's one of those weird things you have to try yourself to understand.
- Fall detection with improved accelerometer and improved gyroscope
- Improved LTE antenna that works through case bottom now in addition to top for better signal strength
- W3 chip and bluetooth 5.0 for faster/further data transmission to iPhone 8/X or newer, which also have 5.0. I suspect that the new AirPods will have a W3 chip in addition to the wireless charging case, which may extend their range and battery life.
- 16GB capacity standard (only on cellular Series 3 or better)
- Ceramic and sapphire back standard (only on SS previously), which has more of a premium feel and I believe is necessary for the ECG
- Gold colorway on SS model for the first time
- It's ~6% thinner, though slightly larger in width and height, equaling the same volume as Series 3.
So you have to see if any of those features/preferences are worth it for you to spend a little more to upgrade to the Series 4. Having just come from a Series 0, I can tell you that the display makes it all worth it. If I already had a perfectly good working Series 3 I'd have not upgraded and waited a year, but if I was forced to upgrade then it would be a no brainer for me. You also have to take into consideration how long you expect to own this watch and software updates, etc, which don't seem like they last quite as long as the iPhone does nowadays. Just look at the 5S and how it has been getting longer updates since it's a 64-bit processor, and the Series 4 now has a 64-bit processor. Furthermore, having a fresh battery from a non-used device is also a nice bonus.
Anyway, hopefully this helps you come to a conclusion about which watch you should purchase.