Cell phone: TIM for Visitors [info]

There are free texting apps like WhatsApp (they use mobile data or WiFi but can't use much data).

To call the US (if you are American) from Europe, use Google Hangouts on your smart phone to make free voice calls, even to landlines. Just make sure you add the "+1" prefix on the front of US phone numbers. It too uses mobile data or WiFi - so technically not "free" unless you are on WiFi, but I've found Hangouts uses about 2MB per minute of data, so still very cheap.

You can walk into any TIM store and buy this plan, you don't have to pre-purchase.

The TIM for Visitors plan clearly states 4GB of data and 100 minutes of talk time.

The Vodafone plan is only for data, calls, and texts in Italy while TIM lets you call other countries.

Thanks for posting your experience.

It may have changed since then but as of June 2016 at least one Vodafone plan included minutes for calls to the US.

We learned, however, that the "100 minutes" is not really "minutes" but an account credit worth 5 Euro

Sorry, but this is wrong. You get 100 minutes of talking time to italian and your home country numbers plus 5 euro of credit.
Either you started calling before the Tim for Visitors had been activated (the plan, not the sim) or you called a special number not covered, or you were out of Italy, or you did not call one of these countries: https://www.tim.it/tim-visitors-countries-en
I doubt Tim is blatantly lying on its site: https://www.tim.it/offerte/mobile/estero/dallitalia/tim-for-visitor-uk Otherwise a lawyer would find it almost too good to be true, they write:

The national voice traffic exceeding the 100 minutes bundle will cost of 29 €/cents per minute with a price based on seconds and with no connection fees. The cost of SMS is 15 €/cents.

Incoming calls and texts are always free in Italy, maybe you texted somebody abroad who pays for receiving texts and calls.

The concierge at your hotel should have asked where you were going after Rome before recommending anything: in rural Tuscany, for example, Tim has a better coverage than Vodafone. If you are visiting only cities like Venice, Florence and Rome the cheap plans offered by Wind-Tre are more than adequate.

The Vodafone plan linked above includes 300 outgoing voice minutes to Italy and your home country if included in the promotion (US and Canada are included).

If you assert otherwise you must come here and produce documentary evidence. The terms of the contract are below. Prove me wrong if you can:
https://www.vodafone.it/portal/Privati/Tariffe-e-Prodotti/Tariffe/Ricaricabili/Vodafone-Holiday-Dettagli-FDT

Regarding the quality of coverage between TIM and Vodafone, the latter has actually a slightly better 4g coverage, but that may vary from area to area. There are some rural or mountainous areas where one has better signal than the other. For example I have Vodafone because in some parts of Tuscany where I stay TIM doesn't have a good signal. In other parts it might be the opposite, but if one stays in major urban areas, all providers work. You can check by municipality below:
http://www.tariffa.it/copertura-rete-mobile/?ASID=LASTAMPA

But overall the two providers have very comparable coverage.