We used Riteway of Calgary to move to BC. Their website says they estimate 15-20% high and we did discuss this when the estimater was there. However we did get a shock when the final bill came in 33% higher than the estimate. If the estimate was supposed to be 20% high then the estimate was out by 50%.
The guys who did the actually moving were great so Allied Van lines would be okay; just don't use Riteway as the agent. Moving is stressful enough without expensive surprises.