The tax softwares all have to comply with current tax law and go through an approval process with the IRS. So....entering the same information should get you the same results. Something you entered was different--somewhere. It is always tempting to believe the higher refund is the "right" one---but we do not know what you entered.
You cannot file twice. If you try to file with the other software it will be rejected. If you think you made a mistake with TT, wait until the IRS has fully processed your return and then amend it to fix the mistake.
It would help you to print the returns -- lay them next to each other-- and compare them --- line by line--to see what is different.
I re-did the calculations on TurboTax and FreeTax several times and still got the same result. I feel like with that much of a difference there's something sketchy taking place behind the scenes.
The only way to see what is different is to put the returns side by side and compare line by line.