The advantage is fit. A hedger with an unusual exposure, an odd maturity or a non-standard underlying can have a contract written to match it exactly, which a standardised listed contract cannot do.
The costs are credit exposure, thinner pricing transparency and harder exit. Closing a position usually means negotiating with the original counterparty or entering an offsetting trade that leaves both contracts live and both exposures on the books.
Post-2008 reform narrowed the gap. Standardised contracts must now be centrally cleared and reported to trade repositories in major jurisdictions, and uncleared trades attract margin requirements designed to make them less attractive. See exchange-traded-derivative and central-counterparty.
Related: exchange-traded-derivative, central-counterparty, isda-master-agreement, counterparty-risk, netting, swap