Is Homestead worth it for current home

[Suneel P.]

I bought an old house in mid July of 2020 in Austin for my primary residence and I have been staying there ever since. I signed contract for another house(new construction) around Austin and planning to move there and rent out the current house. New house is expected to close around August/September in 2021. I want to use Homestead for new house because it will incur more property taxes than old/current house. Is filing Homestead for current house worth it as I am planning to file Homestead for new house (in which case Homestead for current house will be lost) I am going to close later this year?