You can't go wrong with staying under 65C for core temps, and I don't like to have my cpu temps go any higher.
Apparently, I think what SpeedFan and Gigabyte is reporting is the TCase, while Core Temp is reporting, well, the core temps. So while the max temp you can go is 71.4C for TCase, you shouldn't go so high. I'd suggest getting a better cooler or lowering your OC.
SpeedFan 4.34 core readings and Core Temp 0.97.1 readings are about 5c difference.
Which one would be closer to real temperature?
I'm not sure. I'm guessing that the SpeedFan uses the 100C TJunction to calculate while CoreTemp uses 105C. Refer to the temp guide here for more info. In the worse case senario, look at the higher temps, in this case CoreTemps. Then just don't let the temps go over 70C.