Synthetic hydrocarbons requires you either capture CO2 from the atmosphere, or capture, store, and reuse the CO2 of combustion from your turbines (so you're still storing compressed gases underground; you've also made the per-output-power part of your system more costly, which is very undesirable for rarely used backup storage). The round trip efficiency with hydrogen will also be higher, since you don't have to do either of those and the process that makes hydrocarbons starts with H2 and CO2 and is significantly below 100% efficient.
Flow batteries would be better than ordinary batteries, but would still be costly for seasonal storage or rare event backup compared to hydrogen (especially flow batteries using vanadium).
Flow batteries would be better than ordinary batteries, but would still be costly for seasonal storage or rare event backup compared to hydrogen (especially flow batteries using vanadium).