I think the main problem is that the ABI (association of British Insurers) don't actually recognise the existence of an N/A Supra.
The only MkIV Supras on their books are:
"SUPRA TWIN TURBO - Manual" - Group 19 (this is a UK spec)
"SUPRA TWIN TURBO - Automatic" - Group 19 (UK spec again)
"SUPRA RZ TWIN TURBO - Manual" - Grey (Jap import)
"SUPRA RZ TWIN TURBO - Automatic" - Grey (Jap import)
So you'll probably find that many insurers (especially those who only use the ABI groupings) don't actually maintain an insurance rate for an N/A MkIV, and therefore end up putting premiums on it which may (especially for unknowledgable insurance companies) exceed the rate for a TT.
ALWAYS try and find an insurance company who actually understands what car you've got!
The difference in insurance premiums and policies between the two will be pretty much entirely based on how much profit or lost they've made on the two in the past. As you can see from before - the ABI treat the auto and the manual as two different cars, so the corresponding insurance premium rates and policies will be separate too, and will be adjusted independently based on their relative performance as financial products.