A metastable pool is suited for assets that follow an exchange rate with a base asset, like liquid-staked assets such as stkATOM and interest-bearing tokens from lending protocols such as cDAI.
The Stableswap does not consider the constantly changing exchange rate for yield-generating assets and assumes a 1:1 ratio between the tokens. For example, the pool assumes the price of 1 stkATOM = 1 ATOM, as the value of stkATOM in terms of ATOM grows, traders can use this incorrect ratio to leach out the yield from the pool while LPs suffer from impermanent loss.
For example, stkATOM would keep accruing yield in the form of staking rewards in ATOM and would be worth 1.01 ATOM, 1.02 ATOM, and so on.
Metastable pools use stable math along with the known exchange rate for the asset. The metastable pool can take this constantly changing exchange rate into account and hence concentrate the liquidity around the price by changing the slope of the flat part (the price of an asset is the slope of the curve at any point) of the curve, making it capital efficient for LPs and trades more precise.
To access further information on the Metastable Pool AMM mechanism, please follow the link.