There are hardware differences and peripheral differences. What can be accomplished or run on a Model B that cannot be done with a Model A? Are expansion boards being designed to be compatible with both? When available, other than cost, is there an advantage to ordering the Model A?
4 Answers
The model A only has 1 USB port and no Ethernet port, whereas the model B has 2 USB ports and has an Ethernet port.
Although the model B is the only one currently available, the Foundation's aim is to sell the model A at $25 and the model B at $35. Apart from the lower price, model A also offers small advantage of using less power, hence it can be powered by 500 mA power supplies.
Originally model A was only supposed to have 128MB of RAM - but it's now going to ship with 256MB (B will soon be shipped with 512MB for the same price). You may still see references to different memory in old literature.

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1Model A available in Europe as of today: http://www.raspberrypi.org/archives/3215 – Frederic Feb 04 '13 at 12:42
Model A has 256Mb RAM, one USB port and no Ethernet (network connection). Model B has 512Mb RAM, 2 USB port and an Ethernet port. Source ( Under GENERAL )
Also checkout this Wikipedia link for more details ( Under Specifications )

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sice 14.07.2014 the Model B has been replaced by Model B+.
More GPIO. The GPIO header has grown to 40 pins, while retaining the same pinout for the first 26 pins as the Model B.
More USB. We now have 4 USB 2.0 ports, compared to 2 on the Model B, and better hotplug and overcurrent behaviour.
Micro SD. The old friction-fit SD card socket has been replaced with a much nicer push-push micro SD version.
Lower power consumption. By replacing linear regulators with switching ones we’ve reduced power consumption by between 0.5W and 1W.
Better audio. The audio circuit incorporates a dedicated low-noise power supply.
Neater form factor. We’ve aligned the USB connectors with the board edge, moved composite video onto the 3.5mm jack, and added four squarely-placed mounting holes.
The Model A doesn't have a USB hub chip, Ethernet jack, nor a Ethernet chip; has fewer LED lights, 1 less usb port and half the RAM of the Model B; and has one or two very minute differences. However, it uses less power.

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