I get a lot of relocation people and it seems none of them research the state of Texas before moving here. Texas has no state income tax, BUT that means the property taxes are higher than what most people are used to across the county.
Also, taxes are not based on what you paid for the house. Taxes are based off what the county appraisal's office has valued your house to be, which will be very different numbers, in most cases.
Each city, each county, each school, each college, each hospital, etc... has it's own tax value. Many cities split counties and schools so they are not going to have the same tax throughout the city.
I can only educate so much, so please do some research on your own before relocating to Texas or to any other area so you can help yourself understand the differences.