It looks like Arduino is an incredible platform for learning and research. As a fully open arquitecture stuff it is great for research. So I would like to know what are its limitations. Of course, comparing with similar uC.
Arduino is flexible, easy to use combination of software (IDE) and hardware (board and peripherals). It has simpler programming tools with a lot of open source example for implementation of almost any application.
Its hardware capability is changeable and controller dependent. An Arduino platform would be an 8 bits controller (i.e. Atmega 32x, Atmega 16x,) or even 32 bits Arm Cortex M3.
Therefore, it is not making direct sense to compare the Arduino board with another Atmel based board in hardware-wise, because both of them would have possibly the same chip. It is also not making so much sense to compare this software-wise because Arduino IDE is also using AVR compiler on its background. (Maybe some functions would be more efficiently written though.)
On a separate note, if we are talking about comparison between different boards with different controllers such as PIC or Freescale etc. It is not good as way to ask that over Arduino.
At any rate, in my opinion, the beauty of Arduino Platform comes from easy implementation, fast prototyping, and open source. The sufficiency of the Arduino Platform depends on the application that the person has.
Arduino is preferable for its open environment, the software developed for arduino UNO (arduino sketches) can be used for arduino DUE with few modifications. Even the developed Shields (PCBs) can be used in both boards. There is a wide range of shields, spanning from bluetooth and wireless communications to control motor. It is quite easy to develop custom shields for specific applications, They are suitable for rapid prototyping in research applications, of course it depends on the specific case.
I use PIC microcontrollers a lot in my research, and always stayed away from ATMEL ones (the uC used in Arduinos). Reasons are :
a) believe it or not, ATMEL doesn't have any DIP type uC's in their portfolio, so, if you want to hand-solder your own boards (which we exclusively do), PIC is almost the only choice.
b) On the other hand, the opposite argument is true. If you do not want to mess with soldering stuff yourself, Arduino is excellent, somebody soldered it for you, and even figured out a programming language. The language inherently has functions like sin(), however, they could be very ROM-intensive. So, a careless programmer could run out of space quick if (s)he uses these types of functions in a weak Arduino.
c) Using a language like Arduino reduces the portability of your code, and gets you stuck into the Arduino world. This , I found, is the worst part of Arduino language (not necessarily the hardware).
d) I do research with both ECE and CS students. I generally observed that, CS (Computer Science) people love the Arduino's due to the "high abstraction level" of both hardware and software, and ECE people love the PICs, since you can control every bit and byte and use plain old C programming instead of Arduino which adds one additional abstraction layer on top of C.
e) Open support typically means that, you are relying on volunteers, not a commercial entity who you PAID. However, the Arduino community is an amazing bunch of people that are eager to give each other. The complexity of the boards is not that high, so, there is an incredible amount of information (and designs) are available. SO, I would say, this is an ADVANTAGE. Just because you paid someone, they will not necessarily provide excellent service. I found that, once you start asking questions beyond the commercial development boards' cookie-cutter answers, they CHOKE ! So, as far as support, I would say, Arduino is surprisingly better.
Arduino is just a board framework using AVR µC from Atmel, there is a good overview on the types of processors in the German Wikipedia, you will understand that without knowlege of German language. They mainly use the 8 bitters like AtMega128/368/1280 but also one board is the 32 bit version AT91SAM3X8E. These AVRs are so simple, you can just put them on any board you like, there are several DIP packages available (e.g. ATMega88, ATMega 16), we also solder the TQFP by hand.
You dont necessarily need to buy an arduino board for that but is already there. A good alternative if you like AVR is atmel's evaluation boards series. I agree to Tolga that the arduino library is sometimes rather a disadvantage because they consume very rare ROM capacity. AVR is so simple in direct programming and they have good documentation and such a huge community that you will find almost any thinkable solution for that type of processors (they have strong performance limits of course). Look e.g. at www.avrfreaks.net
We use ATMega88 (DIP package) for Basic education for almost 10 years now.