Yes, keep pumping to around 110, give or take some depending on your weight. It is very difficult to determine road bike tire pressure by feel with your hand. Use the gauge.

However.....when you pump up the tire, is the needle moving up high and then falling back down? Perhaps you don't have a good seal in the pump and aren't getting an accurate reading. You might also hear air leaking from the valve if this is the case. I doubt that the same thing would happen with both pumps, though.