According to DXOmark on your K-S1 the Sigma 18-200 outperforms the Pentax 50-200 in terms of sharpness and less vignetting, but the Pentax has better light transmission, less distortion and chromatic aberration. There are many other factors including price, size/weight, and anomalies that come with a wide-telephoto zoom.
Of course nothing beats experience in the field, but in terms of your specific question, the tests indicate the Sigma is at its sharpest wide open at 18mm, whereas the Pentax sweet spot is at the long 200mm end at f/8.
http://www.dxomark.com/lenses/brand-pentax-sigma/mounted_on-Pentax_K-S1-971/...taType=rankDxo