The T51R SPL is actually a better turbo for the Supra... Both the KAI and SPL shares the same turbine specs, but the Supra seems to like a bit heavier on the compressor side.
Compared to similar sized turbos, the HKS T51R's has a huge turbine housing so it will always be laggier to say a PTE71 or 76mm turbos... All the common 71mm or 76mm turbos come with smaller exhaust side to encourage earlier boost, but then response and breathability up at higher RPM's are compromised. Exhaust pressures also skyrocket if you decide to fully use up a 76mm but with a small 0.69 or 0.82 A/R housing.
I personally like the T51R turbos because they seem to breathe so well and allow lots of power on pump gas. It seems like whatever car I put the T51R into, the engine allows way more timing, more boost and more power on the usual 94oct pump gas at Sunoco. The lag is there at low RPM's, but the fact that this turbo is really responsive, it never falls off between shifts. Of course, to whoever that is shopping for a 76mm turbo, cams, valvetrain and a higher redline is mandatory to allow a decent powerband. But due to the HKS T51R turbo and some tweaking with the cam gears w/ HKS 264's, I managed to make power all the way up to 8000RPM.
I don't have dynos of clean comparison between the two turbos because I just recently discovered I had a leaking BOV... All my graphs had a leaky BOV and the spool time is way off... But here's a few graphs:
HKS T51R SPL on my Supra, 50% 115oct and 50% 94 oct, + water/meth
T51R KAI on my Camry, 3.0L V6, 94 oct and water/meth: