I have heard 80% faster In synthetics also you seem to forget 8 Core MTL-H vs 8 Core LNL was 33% difference for the same cores but in TS and some other stuff it was not observable.
You can't compare -H with Lunarlake. You have to compare with similar power Meteorlake. There's 15-20% gap there. Comparing to Meteorlake it's 15% faster even in synthetics. This has always been true, even in the Sandy Bridge days. The -H parts had ~20% advantage.
Arrowlake-H's higher power envelope catches up to Lunarlake even in lots of games.
It will definitely be faster than B580 though for the main reason not suffering from overhead Xe3 is a big overhaul as big as Xe2 was vs Xe1
There's usually a ~20% penalty for the mobile part and the absolute bandwidth is quite a bit less. It's only at 70%, plus it has to share which will be bulk of the performance difference(less effective bandwidth + penalties). It's not a small gap to make up for.
I have rule of thumbs for mobile vs desktop, iGPU vs dGPU:
-If the architecture is well balanced, iGPU is equal to 25% perf difference or roughly 1/2 the memory bandwidth
-5-7% faster per clock for a desktop CPU
-15-20% faster iGPU for -U vs -H