Did Tycho Brahe improve measurements twentyfold? I am reading a book on the Coopernican Revolution where the author states that Tycho Brahe was able to make twenty times more accurate measurements than any of his predecessors.

On the other hand, I remember having heard a lecture where the speaker said that Tycho did not significantly improve measurements since Ptolemy because no new equipment (telescope) had been invented.

So, which statement is correct?
Accuracy relative to other authors is hard to estimate.

However, here's a scholarly article that shows a modern determination of the actual accuracy of Brahe's measurements in absolute terms:

http://adsbit.harvard.edu/full/1978JHA.....9...42W

The conclusion is that it depends on the instrument and it depends on the actual measurement, but as a general rule he was able to obtain an accuracy better than 1 arc minute, often down to 0.5 arcmin.

For comparison, the resolving power of the healthy, young, average human eye is around 1 arcmin. So Brahe was able to somehow make measurements with an accuracy better than the smallest details resolved by the human eye, even though there were no magnifying instruments available in his time. I believe this was achieved by averaging multiple measurements.

In other words, he was very near the limit of what was theoretically achievable before the invention of the telescope. He was certainly the best of his era by a large margin, and far better than distant predecessors such as Ptolemy. What mattered here was the methodology, and the unprecedented scale of the instruments (the armillary sphere, etc).