I am in the reverse situation: I ride a YZ-125 and my 20 year old son rides a YZ-250.
My son is a much better athlete than I ever was, so add in the age factor and a bike of half the engine size it is no wonder that I struggle to keep up.
When we get into the rough stuff I can keep up okay. We occasionally get into a sand wash or come to a double whoop that he can simply gas it and clear the double. I gas it and have to ride through both of them. When we get to the real technical stuff, narrow goat trails and weaving through boulders I have no problems at all. When it comes to the hill climbs we are 50/50. There are some hills that I simply run out of power, fall off the power band and cease forward motion. But there are other hills that I manage to make my way up that my son fails to cliimb.
Where I get left behind is when we hit a smooth trail or fire road where you can really open the bikes up. I shift up through the gears, end up WOT at the top of the power band in 6th gear and just watch his dust fade into the distance.
At some point you may long for a 250. For now, I bet you will really enjoy the 125. Unless your dad is really good and a speed demon you may find that you have no problem at all keeping up.
Rod