So, to address to all points:
Strength: Spino was a piscivore that didn't need any strengh to hunt. It's natural logic that an apex predator like Rex would be physically stronger.
Size: Multiple newer estimates have put the spinosaurus at weights ower than you 20 tons and theey're globally accepted virtually everywhere.
Speed: Again, semi aquatic piscivore vs land carnivore.
Intelligence: Semi-aquatic solitary piscivore vs apex pack hunter land carnivore.
Claws: Nope:
https://pre00.deviantart.net/b254/t...skeletal__msnm_v_4047__by_franoys-dbokpwj.png
Explain to me how he would cause damage with those claws.
And finally, for the nail in the coffin, about T. Rex intelligence:
http://www.dailymotion.com/video/x57t2qc
Sorry for the japanese, but Rex apparently had organized pack hunting behavior with each member having different roles according to their size and age.