Conservatives and people like the Cato institute want them because it would reduce spending on Medicaid. They see it as a redistribution of wealth by shifting dollars from high-income states (such as New York) to lower-income states (such as Mississippi.)
Those who don't like block grants say the more likely results would be state taxpayers being stuck with the tab of ever increasing health care costs or major reductions in Medicaid services that would leave the poor with no good options for care.
1) Hard to react during times of macroeconomic crises
2) Funding inevitably starts to go away while the expenses don't
3) Additional requirements from congress inevitably get added by congress making it harder to for the block grant to serve its original purpose