Depending on what you mean by local, you're never going to be able to directly contact your representative. Your phone call, if answered by a human will be an intern or other sort of assistant who will basically end up marking you as a tally on whatever side of an issue. You will have near zero influence. Emails are even worse. I'm sure now a days you'll get LLM slop but 'back in the day' you'd get a response that always came down to "Thanks for your message. Representative Joe Blow likes good things, and dislikes bad things. And he even thinks important things are important! Thanks for your message, and remember to vote for Joe Blow! Bye!" Even better, you get subbed to a bunch of donation begging mailing lists.

By contrast go buy a top dollar lobbyist, and he'll go endlessly push your issue to all his old buddies. He'll even compose legislation that can be rubber stamped by the reps that your lobbyist will know are most inclined to agree with. You'll get better than direct contact and over a sustained period of time if necessary. I don't think the two are in any way comparable.