1. Seattle's $15 per hour minimum wage isn't the reason the Seattle area has such a strong economy; its strong economy leverages such factors as a highly-educated populace (57% of Seattle residents have Bachelor's Degrees or higher while fewer than 7% lacked high school diplomas), and is a reason the minimum wage increase (just now being phased in) will very likely have a much smaller adverse impact than that in Los Angeles.
2. The law will impact approximately 102,000 workers having wages between $9.32 per hour (Washington's minimum wage) and $15 per hour, or about a quarter of Seattle's workforce: Study: $15 wage floor would lift pay for 24% of Seattle workers | The Seattle Times
3. A study is being conducted by the University of Washington on the effects of Seattle's minimum wage law (Seattle Minimum Wage Study | Evans School of Public Affairs). As the law is just being phased in, data is not available. Some media outlets have been using "concerns" as proxies for data, but the actual data will be essential to measuring the impact in Seattle. Right now, there's no conclusive evidence of a major impact (which may lend support to the modest impact scenario), but it's premature to reach firm conclusions right now.
IMO, Seattle is well-positioned to handle its $15 per hour minimum wage with only modest adverse labor market and broader industry structure and economic effects. Los Angeles, with more than a quarter of its population lacking a high school diploma and fewer than a third possessing college degrees, is in a notably weaker position than Seattle.