As others have mentioned bitcoinwisdom is the one to use. It looks at the last 2016 blocks solved and should be within about 4% of the actual average network hash rate over the last 2016 blocks 95% of the time.
I suspect cryptanalys.is badly in error for a few days after a difficulty change.
The problem with cryptanalys is that it either ignores, or does not understand, the statistic variation in the block solve time.. It basically says we are x fraction of the way through finding 2016 blocks and it took x time so we can now calculate the expected difficulty change. But at the start of a new difficulty it is only using a few blocks in its calculation and the error is large.
For example after one day cryptanalys is only using about 144 blocks and the solve time calculation error and thus error in hash rate can be up to 20%. The cryptanalys error declines as the next difficulty change approaches as there are more and more blocks included in the calculation until finally it is using 2016 blocks.
bitcoinwisdon appears to always use the last 2016 blocks so statistical variation is less important.
When the next difficulty change finally occurs both give the same result as both are using the solve time of the last 2016 blocks.
Mathematically there is a 10 minute block average solve time with a 10 minute variance (poisson distribution). So the standard deviation percentage error in solve time is 100 / sqrt(number blocks). This gives a standard deviation error of 8.3% for 144 blocks (1 day), 4.5% for 504 blocks, and 2.2% for 2016 blocks (difficulty change). The variation will be within 2 Standard Deviations of the true value 95% of the time.
Note - Six months ago, in the high growth rate days, you could have made a case for crptanalys, as on the first day after a difficulty change it used the average of that day, rather than the bitcoinwisdon average for the past 2 weeks. But with a lowering in hash rate growth this is less relevant. The crptanalys error in the first days after a difficulty change is so large it swamps the effect of the data being slightly more up to date.
Feel free to improve or correct my understanding of how these sites work.
I will also track predictions in time so it'll be possible to see which are useful and which are not. If you know about other sites predicting difficulty let me know I'll add them too 
