Does the fuel line/carb prime faster with the throttle at a high setting, like full, when the choke is on?

Or is it better to leave at a low throttle, like 1/4, setting with choke on to prime the system?

I've never noticed much difference between 1/4 throttle or full throttle on priming. Anything off idle will do........

Th way the "choke" works-- is to block most of the air inlet --
when the prop is pulled thru -- the crankcase LOW pressure , tries to equalize (ma nature at work) and the only real source of any higher pressure is in the fuel system of the carb
So------
the fuel flows out of the low speed port - closer to the engine and if the throttle plate is not firmly closed , the high speed port (s).
Once the engine starts to pulse (run ) the carb pumps fuel into it'self and the regulating diaphragm balances "jest right " to sup[ply fuel as needed
What will increase choking flow, is reducingthe size of th bleed hole in the choke plate.
On some engines -unfortunately -the choke hole bleed plate is badly mismatched for a hand started engine
typically- the setup was correct for a rope pulled , faster , group of low pressure cycles in the crankcase.

The carb primes faster with the throttle closed.
This seems to be true for the BME 100.
It has the hole in the choke plate so it is hard to generate low pressure in the crank
I rock the prop back and forth to cause the pump to do it's job.