Samsung released fives smartwatches in the past year - and all of them used AMOLED displays: 1.63" 320x320 Super AMOLEDs in all the Galaxy Gear series watches and a 1.84" (432x128) Curved Super AMOLED in the Gear Fit.
Samsung Gear Fit
Now we hear a report saying that Samsung is set to release yet another smartwatch, the Galaxy Gear 3. It will be based on the Tizen OS, and will sport a rectangular curved (flexible) OLED display. This panel will have a very pronounced curve - significantly more curved than the Gear Fit. The report also says that the display will have an impressive brightness and color saturation.
Samsung Galaxy Gear 2
It seems that Samsung is busily upgrading its smartwatch designs and features with iterative products. It's a very new market and Samsung may be wise in trying out all sorts of products - check the market reaction and then quickly making a new design. According to Canalyst, Samsung clearly leads the smart-band market. Apple is anticipated to enter this market soon, hopefully the iWatch will also sport a flexible OLED.
5 smartwatches in a year and yet the market is miniscule. Even amongst tech geeks the reception has been lukewarm at best...
Persobally as long as the smartwatch needs to stay closely tethered to your smartphone I don't think there will be much of a market there. Someone needs to figure out how to turn the smartwatch into a standalone product.