Can you tell the tech progress of a vassal? Or any other empire than your own?
You can make relatively accurate guess of the numerical difference by count how many researchs you have done then checking the values for each players research agreements then you simply add your total research to the opponents agreement then subtract your aggreement.
((your number of total research + tech only ai has - tech only you have)/ (your number of total research))*100
this will give the percentage tech value of ai race compared to yours.
This assumes that all techs are equivalent. Unfortunatly since you can't give or recieve research agreements from protectorate you can't find out if they are close to your tech level.
Depending how research heavy your empire it is very possible that the protectorate will never catch up to you. (This will be the case if you have 5* their research capacity, or 3.75* their capacity if you have a research agreement with a liberated fallen empire)