We are traveling to Switzerland (mostly Zurich and closeby) for several days later this year and, one of our friends told us to bring Swiss Francs with us as things would be generally cheaper if we pay with Francs as opposed to paying with Euros. Our home currency is U.S. dollars.
Is this actually true?
(keeping it broad intentionally, but please let me know if any additional details are needed)
The currency of Switzerland is obviously the Swiss Franc, not the Euro. Many businesses accept euros, but:
Not that this does not mean you need to buy Swiss Francs before arriving or that you need to exchange Euros for Swiss Francs. Withdrawing Swiss Francs at an ATM in Switzerland will often be the cheapest option (though you should check the charges of your card issuer in terms of exchange rate spread and for foreign transactions).
Likewise, you can pay for many things directly with a credit card or debit card with a balance in Euros (or any other currency). Your card issuer will convert the currency automatically, and if your card has low fees, this will often be even cheaper.
As pointed out by IMSoP in the comments, if when paying by card the retailer (or rather the terminal) suggests to perform the currency conversion for you (this is called DCC – Dynamic Currency Conversion), you usually will want to refuse, as the rate applied is generally much worse than what you can get from your bank.
But again: check the fees for your credit or debit cards before you leave. They're the key to making the right decisions (which may involve getting a new card with better fees!).
It is always less expensive to use a country's own currency when in that country. Merchants lose money on conversion fees when they accept payment in foreign currency, and they typically cover that by using a less favorable exchange rate to figure the foreign-currency price than you will find in the banking system.
Yes, it's cheaper, the exchange rate is not favourable for the client. If you go shopping for currency upfront, you can find a better deal for exchanging whatever you need and you'll paying a one time fee, instead of a fee in every payment.
It's also more convenient. Small businesses won't necessarily accept euros, and they have no obligation to do it. Hotel chains and department stores will probably accept them, shops near the borders probably too. Notice that you will get the change in Swiss Franc anyway.
Absolutely. Every time you exchange money, with anyone, anywhere, anytime, they are going to charge you for the privilege. In my experience, banks give the best exchange rates, especially YOUR bank (if you just use a random ATM, your bank will make the exchange). "Exchange" kiosks are all over the place. The ones in London airport are particularly egregious, last I went. Local businesses that don't specialize in exchange may be willing to do the exchange for free to get your business, or they may not, or they may simply refuse to do the exchange. One thing is for sure, though: They will not give you a better deal in the exchange. Ultimately, it's at their discretion, though, and since they're going to the bank to exchange your Euros later, and they have to pay the exchange fee, I would definitely anticipate that 99% of the time they would at least pass that on to you.
Protip: Most exchanges post a buy rate and a sell rate. (buy_rate - sell_rate)/sell_rate is a good metric for how hard you're being fleeced in the exchange. 0 is a free exchange. 0.1 (is about a 5% exchange rate) is probably the best you'll get anywhere. Some places in "tourist traps" will be up to like 25%.
The answers so far provide you some good insight as to why you might want to prefer cash CHF vs cash EUR. Allow me to add my view on avoiding this altogether.
If you are only travelling temporary and you use cash, they you always have some loss as you can'd budget to the nearest centime. You'll end up leaving with some cash CHF which you cannot use elsewhere and you'll probably keep it as "souvenirs".
I suggest that you take into account using a multi-currency card, like TransferWise*. This way you can keep an amount of USD in your account and the conversion is made every time you pay with it in CHF, at the mid-market rate. This way, you avoid converting too much or too little, and, more importantly, you avoid the unfair conversion rate of the shops and banks**.
As noted by a comment, most credit cards work this way. However, with the credit card of your bank, the conversion is done by them, at a rate that's advantageous for the bank, plus some non-negligible fee. With multi-currency cards, the conversion is done at the mid-market rate and the fee is very small. For even cheaper option, you can foresee a bit how much you will spend and "transform" some money on your card just once, thus your card effectively holding 2 currencies and using the best one for each payment. More details here: https://transferwise.com/gb/borderless/
So if you use a credit card card, the problem can be avoided altogether. And if it is multi-currency, it can be significantly cheaper than your standard bank.
* I am not affiliated in any way, I just like their product.
**Some shops, like the post office, do not accept credit cards, only maestro debit cards
