I do believe there is a slight difference between embedded engineering vs. embedded systems engineering. In my company embedded engineers focus mostly on microcontrollers. The micro-controllers are 8-bit, most of the coding is written in assembly or C and they don't do much other than light leds, keep counters, etc. In contrast, embedded systems engineers work with microprocessors that run embedded OS. It's basically a computer. An example would be the Apple iPhone, which has a 32-bit ARM based processor.

I guess the most fun aspect is that you will really understand how a computer works, from touching on the screen of an iphone to the 1s & 0s to the low level instructions that make a computer work. Another thing that I like in embedded programming is that you need to have a good understanding of different hardware components (UART, SPI, DMAs, FLASH, RAM just to name a few) and also know programming. I definitely prefer programming in embedded systems compared to general purpose computer programming. Embedded engineers do pride in the fact that there are very few of them and the pay is not that bad. An engineer can start with 55-65K & earn 80-100K in 5-7 years.
The future in embedded systems is increasing, as you will see smarter devices...your phone will talk to your car, sync music as you go on a road trip, alert you that you left your house with the lights on and remotely let you turn off your heater and lights through smart speech recognition. Your average car these days has more lines of code than an F-16 fighter!
 
The most difficult part I would say is debugging in hardware is sometimes a real pain. Also there are a lot of critical aspects. I your program crashes that might mean a life & death situation...think of the micro-controller that has to deploy the air bag when a sensor detects that there has been an impact. 


I can go on and on but I don't want to bore you to death with...

Good luck,

FF