Depends on the level of difference, the nature the ethnic groups and the how the situation changes. For instance New Zealand's sustained a higher rate of immigration (per capita) than Sweden every year since 2000 (latest figures 2016).
However the impact has been substantially different because of the ratios of refugees to skilled migration. Nor is it a case of one ethnic group staying the same or deteriorating. Maoris have been slowy closing the gap with New Zealanders of European backgrounds in every parameter outside income, and the
increase in that gap is in terms of relative, not absolute performance. There's also less resentment of indigenous groups for obvious reasons.
Likewise in Australia, it took about 40 years for the Vietnamese refugees to bridge a similar gap, but the rest of the groups immigrating vary, for instance with Chinese, Korean and Indian immigrants significantly outperforming the general population. With our ratio of skilled labour immigration to refugees higher than 10:1, I don't think it's an issue.