I like many others used to find it very difficult to distinguish between the two butterflies, but now after lots of practice it is not so bad. I tend to use the following guidelines (Please click over sketch to enlarge).
Also check out these photos to show examples side by side: (Click over to enlarge and click again to supersize)
The Dark Green Fritillary on the left of these photos, shows the first black spot on the right forewing, just slightly smaller than the others and dropped down just a little, the fourth spot is very small, but still in a reasonable alignment to the rest of the line. Also there is little in the way of a depletion to the centre edge of the forewing, (perhaps just the slightest).
Yet with the High Brown Fritillary on the right of these photos, you will note again the first dot is small and dropped very low and then you have two average size spots and then another small spot, which is out of alignment with the rest. Also you can probably note the depletion dip in the side of the forewing, whereby with the Dark Green, the forewing edge is more rounded.
The Dark Green underside of the hindwing, is far more dusty green in colour. And also you can see there is white/silver spots to the full trailing edge (7 prominent spots) of the hindwing underside.
The High Brown is far more of a general brown appearance, with far less of the dusty green. And it only has 3 prominent white/silver spots to the full trailing edge (3 prominent spots). Also the High Brown has a row of silver pupilled red spots which show vertical behind the 3 prominent white/silver spots.