Alexa and Compete are wrong in much the same way a clock is never right. It's a nearly impossible task to properly rank sites in that particular way, there are just too many variables and many of them have 'unknown' as their current value. Sampling the way they do is quite imperfect.
That said, as tools for relative comparisons they're quite useful, as long as you put a sufficiently large gray area around the results (50% or so). That way you can compare sites in magnitude without getting bogged down over whether a site at rank 1200 is larger than a site at rank 1201, the difference is small enough to be meaningless.
The final way in which you can use them is to use their time series to determine a trend. And that's where both are very useful, because assuming their sampling method is the same over time and assuming that there is some significant relationship between all the traffic you're interested in and the portion sampled the trend will be quite strongly reflective of what is actually happening. So growth, stagnation and decline can be determined with some accuracy (you still have to do some smoothing out but on 'max' with Alexa and a site that's a couple of years old the trend will be clearly visible).
That said, as tools for relative comparisons they're quite useful, as long as you put a sufficiently large gray area around the results (50% or so). That way you can compare sites in magnitude without getting bogged down over whether a site at rank 1200 is larger than a site at rank 1201, the difference is small enough to be meaningless.
The final way in which you can use them is to use their time series to determine a trend. And that's where both are very useful, because assuming their sampling method is the same over time and assuming that there is some significant relationship between all the traffic you're interested in and the portion sampled the trend will be quite strongly reflective of what is actually happening. So growth, stagnation and decline can be determined with some accuracy (you still have to do some smoothing out but on 'max' with Alexa and a site that's a couple of years old the trend will be clearly visible).