Akro, I am not sure I can agree with the different curve bit, the TIT is always a higher number but as for lagging significantly behind relative to fuel flow left to right, not so much.
I've had a fair bit of trouble getting real data on this. There is a bit in the Bosch Automotive handbook and I've found a couple of old NASA papers. But none of it is definitive. For engine calibrators & researchers, TIT and EGT are crude measures. Its only pilots who are stuck trying to operate with them!
We should really be moving toward installing lambda gauges. Then we could measure the A/F ratio rather than use EGT as a proxy for it. If I had an experimental aircraft that's what I'd do. For my certified twin, I'd rather have a go at reconciling the Russians & Chinese than go through the STC process.
TIT is higher than EGT because is a more constant flow of hot air. The EGT probe is allowed a fraction of cooling in between pulses It measures temperature a bit like measuring RMS AC voltage.
TIT appears to peak 25 - 50 degF after EGT. But I'm not sure why. I can imagine that the temperature in the exhaust pipe would be a complex thing that behaves differently ROP & LOP and at different gas temperatures & flow rates. Some ROP conditions will have continued burning of the charge in the exhaust piper for example.
I believe the TIT curve will be a bit "flatter"and less "peaky"than EGT. But its at the margin really.
Which is an opening to talk about gauges. A stock analogue gauge using a k type thermocouple is lucky to be with 100degF and its calibration curve will be non-linear. I calibrated our stock Alcor ones and they are within about 10 degF in the operating range after fettling, but outside that it very quickly deteriorates. The digital gauges are a lot better, but not all are cold junction compensated and I challenge you to discover which are! Without cold junction compensation they can vary by the change in ambient temperature from the calibration temperature - in other words up to probably 50 degF. The trends count more than the absolute readings.
This impinges on the TIT debate. There is no point in being hung about about being degree perfect on an instrument that will probably have 50 degF error.
I think manufacturers install TIT gauges to protect the turbo, then they get used as a proxy for EGT for the purpose of leaning. The proper thing is to install an engine analyser and use EGT for leaning and the TIT to monitor turbine temperatures to protect the impeller & housing.