If you force a side to cede control of a hold, the other will gain control of it. This has a few effects.
A hold changing sides will replace the Jarl with either an Empire or Stormcloak loyalist as appropriate. This removes any bounty the Dovahkiin has in that hold. It does not reset progress with Thane-related quests which will continue with the new Jarl
If and when you do the Civil War questline, the quest for any hold your faction holds is skipped. This means you may have to do more or fewer quests before the final battle for Solitude/Windhelm. The War Hero achievement is tied to taking Markarth/Riften- it is permanently missed if your side takes it in this negotiation.
Finally, if the Dovahkiin has chosen a side and brokers a favourable treaty for their side, Ulfric/Tullius will give them a levelled weapon as a reward. They will chastise the Dovahkiin if they negotiated a bad deal but there is no further effect.