When selecting a shoe for running off-road you need to look at the terrain you`l be running over then match a shoe to it... eg
Adidas Adizero XT3: great shoe for when the trails are baked dry or mixed terrain runs with a mile+ of road work..can deal with an inch of mud but lateral grips not great
Inov-8 X-Talon 212 : Serioulsy capable off-road shoe thats light, flexible, with superb stability for running muddy/technical trails at faster than an MTB pace..
Inov-8 Oroc 280 : Amazing off-road shoe that grips wood/rock/snow/ice like you wouldn`t belive..