I like the Subaru BRZ and the other Toyobarus, they're very good at handling due to their superior chassis compared to other sports cars like the entry-level Camaro and Mustang models, the Audi TT, BMW Z4, Mazda Miata, and even Lotus Elise.
The problem is that Subaru and Toyota have wasted too much money on outdated cash cow jokester cars like the crap handling 5.0-liter Lexus F models (which get severely punked by turbocharged German market competitors) and the boy racer GR hatchbacks (which also are HORRIBLY FASTER than the weak BRZ). They could have developed an STI version based on the BRZ with the WRX sedan's powerplant while retaining the RWD system, but instead they went the whole other, useless route.
My advice to Toyota (AND ESPECIALLY NISSAN) would be to save this "rivalry" s**t for the Americans and Germans. The Japanese should focus on producing better handling cars. Look at Honda for example, they have the Civic Si and Type R, both great budget-friendly hatches that will trap you nowhere on a highway. The Acura TLX Type S will kick asses of the Lexus and Infiniti V6TT and V8 sedans on twisty tracks because of its superior package (tires, wheels, brakes, suspension, even appearance is important).
And then there's that boring AWD GR Corolla, which is a bit more of a premium performance hatch than a driver's car. Closer to a grand tourer than a sports car, to be real honest...
The Japanese made very decent straight-line cars during the '80s, '90s, '00s... many of them were credible track cars too. And then the Subaru WRX STI when it first came out went from killing muscle cars to barely being on par with I4T and V6 "muscle cars"...