When we compare Dyson DC35 and DC31, we can find some differences between Dyson DC35 and DC31.

images from manufacturer

Dyson DC35 vs DC31:

1, Battery Life.
DC35 has a longer bettery life than DC31 in standard mode.
Both of these two vacuum cleaners are powered by lithium-ion battery and have dual power mode, but
Dyson DC31 runs 10 minutes on 38 airwatts and 6 minutes on 65 airwatts while Dyson DC35 runs 15 minutes on 28 airwatts and 6 minutes on 65 airwatts.
Though DC35 Multi Floor has better run time, you can also see that DC31 has a 38 airwatts suction power in regular mode while DC35 has only 28 airwatts.
If you check out the battery for these two vacuum cleaners at dyson.com, you can find that they both use the same battery – Part No. 917083-01.

2, Floor Tool and Wand.
DC35 has a motorized floor tool with carbon fiber brushes for picking up dirt from hard floors and rugs/carpet; and it also has a detachable aluminium wand for cleaning high & low areas, and awkward spots.
But DC31 does not come with these tools.

3, Price.
Dyson DC35 is more expensive than DC31.
At dyson.com, Dyson DC35 price is $299.99 while DC31 price is $219.99. (on July 13, 2011)

4, Weight.
DC35 is heavier than DC31.
DC35 weighs 4.96 lbs while DC31 weighs 2.9 lbs.

5, Color.
DC35 is blue while DC31 is yellow.

6, Dimensions (height x depth x width).
DC35 dimensions: 44.1 x 9.1 x 11.8 inches
DC31 dimensions: 12.7 x 4.5 x 8.07 inches

7, Wall Mount.
DC35 has a wall mount while DC31 does not.