Ok, im an FMG and I have two options of doing volunteer research at my home institution. in one of them, the PI has connections to a university in the US (she's an assistant research professor at the department of internal medicine). in the other, this guy is like one of the biggest person in his field in the country. which would be better if i wanted a strong booster for my residency application? or more generally, are 'connections' important in residency applications?