How important is a polished/pretty prototype to pitch an idea to potential customers and/or investors? I'm using this as a means to support my pitch.

It depends how clear your idea value is without it, or with a rough one, or mock ups vs polished.
There are a few goals you are trying to conquer with a prototype, overall its about concept clarity and valuation.
1. customer/investor acceptance: "i want that"
2. customer feedback: "you should change that"
3. investor valuation: "wow, you are that far along" vs "its just an idea"
Without more details only you know what it will take to get the right clarity to the customer and investors to answers on above.

More important than a polished prototype is to first polish your skills with regard to your ability to generate and communicate ideas.

Once you have accomplished this then you must figure out who is your audience. Crafting a pitch without an audience in mind is like addressing a love letter, "to whom it may concern".

With regard to the technical execution of your pitch, below is a link to some of my pitch videos. The audience of these pitch videos vary and therefore so does the style of the pitch.

http://www.jaredjoyce.com/licensing.html

Once you have decided who is your audience and have reviewed my pitch videos, schedule a call with me and I can help you craft your pitch video that will best trigger your investor hot buttons given your specific variables and situation.

In pitching to an investor, in general, I'd say that you are better off with an idea with more customer validation done and a rough prototype than you'd be with a polished/pretty prototype that has no/minimal customer validation.

In pitching to potential customers, at a minimum, the prototype has to do enough to engage the customer, help them see (actually or help them easily imagine) how it solves their problem.

The thing to watch out for is muted reactions from customers, e.g. "Yes, I guess we could probably use this." Instead, you need to be able to elicit this, "Oh my God, this is great...by when can you make this a fully functioning version."

Without much context about the product/company (and whether its B2B or B2C, etc.), it is hard to provide specific advice/suggestions, but hopefully the above help give you an insight into my thinking. Happy to discuss more if you'd like to.

In brief: "Not very."

It's much more important to demonstrate a rough, working product that has customers willing to use it rather than a shiny prototype that has no customers.

By the time you're seeking VCs or angel funders you should be able to speak in terms of how many people are using the product and what your real expectations of a customer base are based on real-world feedback.

The question you need to be asking potential customers is less "would you use this?" and more "how would you use this?", "what would make this perfect for you?", and "how would this change the way you do things now?".

To this end, get a minimum viable product in front of customers and run through the build-measure-learn feedback loop. Accelerate the application of your learnings into the product, get some passionate early adopters and build a community of support that you can then take to investors as validation of the ideas.

Of course, you could also learn from this exercise that your product isn't that interesting to customers. Better to learn that cheaply rather than after sinking a lot of money, blood, sweat & tears into a polished/pretty prototype.

Good luck!

It all depends on recipient skills, experiences, imagination and expectations… and of course on your explanation and purpose of whole presentation.

If you are presenting content-related solutions, it's much more better to work with raw sketches. If it's clear that visual design is not the topic at this time, it's much more easier not to be tempted to talk about "how it looks" instead of "what it is", "how it works" and "why".

A prototype is crucial at seed stage. It depicts your ability to solve a problem through your effective solution.