End Result: Over all Sony Cyber-shot H20/B is better – Details Below
Same Features in Sony Cyber-shot DSC-H20 & SX120 IS:

Almost same Megapixels 10.1 & 10
Same 10x Optical Zoom
Exposure compensation in same -2 to +2 EV in 1/3 EV steps
Same 3" LCD
Same LCD pixels 230,000 (LCD quality is same)

Difference & Comparisons of Sony Cyber-shot DSC-H20 & More >