Tyrannosaurus vs Spinosaurus

Could you provide some links to the new estimates?

That’s because it is not said in Ibrahim et al. 2014, its an unofficial estimate we don’t know the method of (my guess is that there is no proper method, otherwise it would have made it into the paper).

I did read the paper (it’s two pages long!), and I assure you, it’s not there. The only remark they make about its size is that being over 15m long, it was the longest theropod.
Regarding whether the estimate is valid, I think if they had actually made proper weight estimate, it would have probably been included along with the lenght, so I doubt they actually did. Or perhaps they did, but considered other giant theropods even lighter.

I’ve already posted two sources for even volumetric estimates of FMNH PR 2081 coming out at slightly above and slightly below 6t respectively; Paul 2011 and Stevens et al., cited in Stevens et al. 2008. And what if they didn’t make any estimate and 6-7t was just a guess?

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References:
Paul, Gregory S.: Tyrannosaurus, the Lean Killing Machine. www.plosone.org/annotation/listThread.action?root=16371 Accessed 12.10.2014
Stevens, Kent A.; Larson, Peter; Wills, Eric D.; Anderson, Art: Rex, sit: Digital Modeling of Tyrannosaurus rex at Rest. In: Larson, Peter; Carpenter, Kenneth: Tyrannosaurus rex the Tyrant King. Bloomington (2008); pp. 193-204

I wouldn’t put too much confidence in that. As I wrote elsewhere, broly’s work is good.
But based on MSNM v4047 being 77-96% the linear dimensions of the Baryonyx holotype (based on Baryonyx’ skull lenght being between 90 and 100cm this→ and my own skull restoration), the former’s humerus would have to be 85.5-94.7cm or 82.0-90.7cm in lenght (depending on whether you trust the measurement taken by Charig & Milner or the one by Sereno et al. the figures used in the next paragraph being greatest preserved lenght).

NMC 41582 definitely differs from Baryonyx in proportions→, being longer and anteroposteriorly deeper in proportion to its mediolateral width, so we cannot really be sure that it is Spinosaurus to begin with (although I personally find it likely, more likely than that it’s a sauropod at any rate, and being a theropod, a spinosaur becomes the most probable suspect). Based on my scaling it would be about 81.8cm long.

So keep in mind the skeletal you are referring to is based on a relatively superficial description of the new remains and abbreviated documentation of the methods only, and will probably be subject to revision once they get described in detail. For example, I could imagine the humerus in the skeletal he used as a reference was quite far from

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References:
Charig, Alan J.; Milner, Angela C.: Baryonyx walkeri, a fish-eating dinosaur from the Wealden of Surrey. Bulletin of the Natural History Museum, London (Geology), Vol. 53 (1997); 1; pp. 11-70
Sereno, Paul C.; Beck, Allison L.; Dutheil, Didier B.; Gado, Boubacar; Larsson, Hans C. E.; Lyon, Gabrielle H.; Marcot, Jonathan D.;  Rauhut, Oliver W. M.; Sadleir, Rudyard W.; Sidor, Christian A.; Varricchio, David D.; Wilson, Gregory P.; Wilson, Jeffrey A. (WTF? That paper is less than 5 pages long!): A Long-Snouted Predatory Dinosaur from Africa and the Evolution of Spinosaurids. Science, Vol. 282 (1998); No. 5392; pp. 1298-1302
www.deviantart.com/art/Spinosaurus-aegyptiacus-skeletal-reconstructions-483433951

Quoted from Maganuco;

I can say that the body mass estimate for the reconstructed adult Spinosaurus is between 6 and 7 tons. It was written and discussed in the first version of the manuscript, but not included in the very trimmed final version. It will be included in the next more detailed papers.

The old reconstruction was less accurate. We did not know the new skeleton and its proportions at that time (2005), so we were forced to include in our reconstruction many elements from Suchomimus and Baryonyx just to have an idea of the size of Spinosaurus. In the 2005 reconstruction the body was slightly bigger respect to the head, and the legs - above all the thighs - were way bigger than now. I hope we will have more material for the next reconstruction, but I think that the size and proportions will not change too much. The important thing is that the adults of Spinosaurus attained a considerable size, but they were not heavier than tyrannosaurs and large charcarodontosaurids (based on my observations on the specimens I would say that the largest specimens of Tyrannosaurus was heavier than our reconstruction of the adult Spinosaurus).

Tyrannosaurus wins simply because it was built to. Spinosaurus was a natural fisher, none of the weapons it had were built for combat, since its rivals (Carcharodontosaurus and Bahariasaurus) didn't go for the same animals. Tyrannosaurus was the smartest and one of the strongest giant theropods ever, Tyrannosaurus wins 75% of the time. Spinosaurus only wins sometimes because of the sheer size.