Choosing Diamond or not, depends on your tread pattern. If you have more mud paddle style tire tread with "valleys" running across the tire, normal ladder chains can get down inbetween the lugs. The diamonds prevent this... that is their only reason for that design. Normal lug tires, or tires that dont have a valley straight across the tire section, work fine with regular chains.
For example look at a popular atv tire: MudLite's. You can visually see how ladder style chains could fit between the lugs making them useless. A diamond chain would work better on this particular tire.
If your chains are slightly oversized, you can run the outside offset from the inside, making for a bit more "diagonal" fitment of the "ladder" that can help avoid slipping between the lugs. This ONLY works on tires with big lugs for the chain to hook into on the edge of the tire... otherwise they will eventually align inside to outside, which will loosen the entire chain.
All depends on your tread pattern.