Official Raspberry Pi Page
Core Differences To The Raspberry Pi 1
ARM V7 instead of ARM V6 processor architecture. (This opens it up to operating systems like Ubuntu, robot operating system, Windows 10, etc).
Quad core instead of single core processor. For the operating system and multi threaded applications this provides a massive speed boost.
900MHz instead of 700MHz CPU clock.
1GB instead of 512MB of RAM.
V1.2 of the Raspberry Pi 2 Model B no longer uses the BCM2836 SoC (which contains a quad-core ARM Cortex-A7 processor). Instead this PCB now uses the BCM2837 (which contains a quad-core ARM Cortex-A53 processor). Old versions of Raspbian (pre October 2016) will not work ( the RPi simply won't boot)
Original (pre V1.1): Broadcom BCM2836 ARMv7 Quad Core 32bit Processor, running at 900MHz.
V1.2 PCB: Broadcom BCM2837 Quad Core ARM Cortex-A53 processor.
GPU is the same as for the original Rasperry Pi (it was already a very good GPU):
Capable of BluRay quality playback, using H.264 at 40MBits/s.
Has a fast 3D core accessed using the supplied OpenGL ES2.0 and OpenVG libraries.
Provides Open GL ES 2.0, hardware-accelerated OpenVG, and 1080p30 H.264 high-profile decode.
Capable of 1Gpixel/s, 1.5Gtexel/s or 24 GFLOPs of general purpose compute and features a bunch of texture filtering and DMA infrastructure.
That is, graphics capabilities are roughly equivalent to Xbox 1 level of performance.
4 USB ports
3.5mm jack for audio and composite video out
Compatibility with original model
Increasing the number of processor cores has resulted in a change of processor architecture and new Linux Kernel. The former Pi processor was based on an Arm 11 V6 architecture, the new Pi 2 has an ARM Cortex A7, V7 processor architecture. To maintain continuity with the current operating system, there will be a new operating system build to accommodate the change of Linux Kernel. Other than that, it is almost identical to the currently available O/S and can be used across all Raspberry Pi models.
Raspberry Pi model A and Compute Pi
The official word seems to be "There are no immediate plans to upgrade these to the new Quad Core processor" but it seems unlikely these won't be upgraded in due course. Maybe there's a backlog to sell off first :-)
More processing power = more power consumption.
Original Raspberry Pi Model B peak power consumption: approx 3 watts
Raspberry Pi Model B+ peak power consumption: approx 2 watts.
Raspberry Pi 2 Model B peak power consumption: approx 3 watts (quad core processor with a 6x increase in processing power.
Raspberry Pi 2 Model B idle power consumption: approx the same original model.