There are a LOT of minor difference but I will list one one MAJOR adv from each camp.
For travel photography, night scenes where you DON'T have a tripod, I think the E-3 has a BIG adv, in that you can get the 11-22mm lens and shoot at a WA of 22mm (after conversion to 35mm frame) f2.8, ISO800, 1/3 shutter speed, handheld.
At 2.8, ISO800, 1/3 shutter you can SHOOT a LOT of night scenes. This is something the D300 CANNOT do.
Conversely, if you want a 15mm WA, the nikon camp has a cheap and economical 10-20mm sigma lens. For 4/3rds you have to buy the 7-14mm which is more than 2x the price and cannot mount a front filter (it is a big protruding front element.... I don't think I will be comfortable carrying that lens travelling).
PS: if you can get both at the same price, get the D300. I thought the D300 is more expensive than the E-3?