“Connect to” vs. “Connect with”: Which is better?

"Connect to": often used with things and devices like computers.

Your computer is connected to the internet.

or

The printer is connected to the computer's USB port.

or contexts like these.

But "connect with": often used with people, e.g. someone connects with someone.

Both occur. The version using connect with is more common than the one with connect to, but not tremendously so. Connect to does appear a bit newer though.

Here is the Google N-Gram for connected to/with the audience:

Here are some examples using to:

1. ... impersonations, and planned-out scenarios (which rarely go as she intends), but in order for the dynamic of inequality—of otherness—to be maintained, Lucy remains connected to the audience, not the performers.
           ―I Love Lucy, Lori Linday

2. Simultaneously in the background, I saw myself composed and connected to the audience. My message and delivery were riveting. In that split second, I decided to filter out the images of failure and filter in the images of success.
           ―Change the Way You See Everything Through Asset-Based Thinking, Hank Wasiak and Kathryn D. Cramer, ‎2006

3. They were very connected to the audience.
           ―Kiss My Arse: The Story of the Pogues, Carol Clerk, ‎2009

4. I got solid laughs, but I didn't feel connected to the audience. It's like having sex without the orgasm. It's nice, but, come on, we all know why we step up to “the mic” in the first place. Release!
           —Getting Married, Teresa Alan, 2007

While here are some examples using with:

1. It will also make you appear relaxed and connected with the audience.
           ―The Creative Business Guide to Marketing: Selling and Branding Design, Cameron S. Foote, ‎2011

2. Although the number of songs he knew on the piano were limited, he connected with the audience and was asked therefore to play regularly. His next job was playing the piano with Ed Janis who played the violin.
           ―Pennsylvania Biographical Dictionary

3. Morrison removed from his briefcase a binder containing the speech he had given from memory that afternoon and began to make a few notes in places where he thought he had not connected with the audience.
           ―O: A Presidential Novel, Anonymous, 2011

4. I felt deeply connected with the audience of military brass. After my speech, the admirals congratulated me and said to let them know if there was anything they could ever do for me.
           ―Forgotten Fundamentals

Connect with your target audience.

Connect with : to Relate

Connect to : to join

e.g. : Can I connect my printer to your computer?

"Bound up with" can also be used instead "connect with".

I would suggest that 'connect to' implies a smaller thing being physically joined to a bigger thing. "This aerial is connected to my car." (Your car is also connected to the aerial but you wouldn't put it that way.)

To 'connect with' implies something more ethereal, less physical and something that works both ways. "I really connect with my doctor." (If you were 'connected to' your doctor you would think there was a physical tie between the two of you.)