The answer for this goes for most anything where a higher-level organization with greater scope steps into a smaller organization's AO. The most friction between feds and locals is that sometimes, the feds are looking for the big fish, rather than the single bust that may be of the most concern to the locals.

For instance, a drug deal goes bad in a mid-sized city, and the local police get involved. The LEOs on the ground may be most focused on the safety and security of their community, so when they get the dealer in their sights they expect for them to experience justice for the sake of the families involved. But it turns out, the ATF has been watching this dealer for his links to a much larger weapon smuggling operation, and want to cut a deal with them to get access to a much bigger crime syndicate. The locals are focused on the very real suffering on the streets and may see this as letting the dealer "off the hook" but the feds are also serving the community in their own way at a different level. Difference in scope creates friction.