When i guard, try to avoid using a closed guard... play open guard more, make sure you utilise good hip movement. Use your speed and the agility that an open guard affords you, rather than trying to shut him down in closed guard. Forget armbars and triangles, etc, instead focus on sweeps and chokes... some other submissions tend to work well, such as the bicep slicer, calf slicer and foot locks. Generally though, i'll aim for the sweep.
When on top, stay light, move from position to position rather than trying to pin him. So instead of hanging onto side mount, spin round to north south when he begins to escape. Again, chokes with best, particularly if you are grappling with a Gi. The success of armbars depends on just how strong they are but they'll work on most big guys... you just need to put some extra focus on technique. The keylock also works well for me from mount. Still, when on top against i big guy (i weigh 145lbs) i tend to just go for chokes.