Jefferies now prefers Antofagasta over copper peer Kazakhmys and has downgraded its rating for the latter from 'buy' to 'hold'."Our preference this year for shares of Kazakhmys over shares of Antofagasta has been based entirely on relative valuations (Kaz is much cheaper). However, after reviewing 1H12 operating results, we conclude that Anto's valuation premium relative to Kaz is fully justified, and we are downgrading shares of Kazakhmys," Jefferies said on Thursday."Steps forward for Anto, steps backwards for Kaz," the broker said, highlighting the difference in the two miners' first-half results released recently.Antofagasta's figures were "relatively strong": copper volumes up more than 16% year-on-year, cash operating costs down over 6% and underlying earnings per share (EPS) just 7% lower despite declines in copper prices. However, Kazakhmys's results were "much less impressive": copper volumes were down 4%, cash operating costs up 84% and underlying EPS was 64% lower.Meanwhile, Jefferies reckons that Kazakhmys's 26% stake in fellow miner ENRC is unhelpful. "Unfortunately, Kaz is only receiving a small dividend from ENRC, and this stake is highly illiquid and probably impossible to monetise for now. We are concerned that this investment may continue to be a drag on Kaz as ENRC is highly exposed to steelmaking raw materials (ferroalloys and iron ore), which have been extremely weak recently and may remain weak in the near-term."The broker has reduced its target price for Kazakhmys from 900p to 650p. As for Antofagasta, its target price has been hiked from 1,050p to 1,200p, though a 'hold' recommendation has been maintained. BC