Grease is fine for low(ish) speed applications, in which dirt can be kept out. Too much grease and/or too high a speed will cause the bearing to run warm or hot. This isn't going to happen in this application, in which retention of lubricant is probably the prime concern. Oil has a habit of dribbling away. So grease is good.
Oil is good for high-speed bearings (eg high-speed spindles), particularly if it circulates. It will carry heat away from the bearing, and, with luck, muck too. But few machines we are likely to come across will have oil pumps…