Tough one... The Delica and Mini-Grip are two of my favorite EDC knives.
Blade: The FFG on the Delica and the high flat grind on the Grip both make for excellent slicers. Both feature a great steel (VG10 & 154CM for the main line models). The thumb hole and large thumb ramp on the Delica offer great ergonomics, but it also makes the blade wider (more surface area and drag from friction when cutting). I'd call this one a draw.
Handling / Ergonomics: Both have comfortable handle. The Delica's is a little longer, which does offer a slightly better fit (good, comfortable 4-finger grip, at least with my hands). The Grip's slightly rounded handles are very comfortable, and if I move my fingers closer to each other, I can still get a 4-finger grip on the handle. The shape of the Delica is less conventional, but it is a very functional design. The very pronounced thumb ramp allows for excellent blade control when making precise cuts. The Delica feels like a great amount of effort has gone into refining the design and ergonomics for function. I'd give the Delica the advantage here.
Carrying: Both are roughly the same thickness and weight, but due to the curved handles on the Grip, it does swell a little wider (maybe 1-2 millimeters) in the center. The Grip has a smaller footprint than the Delica. Both sit comfortably and unobtrusively in the pocket. The Delica does offer tip up or down carry, but the Grip is tip up only. Both can be swapped for left or right carry. I'd call this one a draw as well.
Lock: Both locks are well implemented and plenty strong. The Axis lock is faster to disengage than the back lock and gives you the option of waving the blade open and closed, if you so choose. I'd give the Grip the advantage here.
Cost: Benchmades seem to carry a higher cost premium (be it branding, proprietary Axis lock, or who knows). Advantage goes to the Delica here.
Pic (top to bottom): Ritter Mini-RSK1 w/ Wilkins scales. Benchmade Mini-Griptilian w/ OD handles and D2 blade. Spyderco Delica4 FFG.