Either party may seek appellate review of the judgment for compensation of the damages awarded in the superior court within thirty days after the entry of judgment as aforesaid, and such review shall bring before the supreme court or the court of appeals the propriety and justice of the amount of damage in respect to the parties to the review: PROVIDED, That upon such review no bonds shall be required: AND PROVIDED FURTHER, That if the owner of land, real estate, or premises accepts the sum awarded by the jury or the court, he or she shall be deemed thereby to have waived conclusively appellate review, and final judgment by default may be rendered in the superior court as in other cases.