Eurorail v. Driving a car?

Renting a car and crossing into multiple countries has many pitfalls. First is the expense - your costs will increase with every border crossing. Second, driving a car in a European city can be a nightmare. Street signs are difficult to read and the odds of finding affordable parking can be astronomical. You also run the risk of getting parking or even speeding tickets, especially in Italy, and you won't know how to pay them but if you don't, you run the risk of it getting back to the rental car company.

The upside, of course, is the flexibility, but I'll be honest; I don't think that negates all the downsides to it.

If it were me, I would rely on train transportation as much as possible. If there are places you want to go that are difficult to reach by train, consider renting a car for a few days in that area. I did that in Germany last year - I was there for a month and mostly got around by train, but rented a car for four days when I was visiting a small town that would have been hard to access by train.

With regards to a Eurail pass, you can do the math and see which works out better for you. Eurail passes have the advantage of flexibility but they are expensive. It might be cheaper to just buy point-to-point tickets.

It all depends on where you want to go. If it is well served by rail and perhaps bus then that is what you use. If it is well off the beaten path, then you use a car. And you could use the train for major travel between cities and renting a car for a day or two for shorter trips. Generally obtaining a car in one country and dropping in another is very expensive and rarely makes sense to do so. You might consider renting in one country and drive to a border city, drop the car, cross the border and rent another car. Also remember with the car you have additional costs -- often overlooked -- fuel, road tolls. and the final prize -- the parking tickets after you return home.

And, finally, Eurail is a travel agency and not a train company that sells the Eurail rail pass. Assume that is what you meant by Eurorail pass. These days of advance purchase, deep discount train tickets coupled with seat reservation fees, a rail pass is more of a convenience than an economic savings.

There are other options as well. But I would strongly recommend the train, although single tickets can be a better option. If you want to visit somewhere really out of the way, you can rent a car for a day or so.

Have you read our host's free Travel Tips?
https://www.ricksteves.com/travel-tips

You may benefit from listing the stops you hope to make, even if you eventually need to eliminate some of them. Is this your first trip to Europe? You may want to go to the library to read our host's books on Spain and Italy, because he covers the travel-basics in a great way.

Edit: Your use of the term Eurorail may just be a shorthand. But note that you do not want to buy air or train tickets from a third-party reseller (with a catchy name like that.) Some people here seem to use Deutsche Bahn for any European country, but I usually use the national rail company for the place my train is leaving from.

It's all in the details--where and how long. If you plan on not following the train line and traveling more than a month, you could look into leasing a car.
For just about any other scenario, the train is the best option. You could always use the train primarily, and then divert using a car for a portion where it makes sense, as others have already suggested.

....and the final prize -- the parking tickets after you return home.

Frank isn't kidding about that, at least not in Italy. To avoid some nasty fines, it's imperative that you do your homework about driving & parking so that you understand the signage and where you are, and are not, allowed to do either of those things. Motor violations (speeding, driving in bus lanes or ZTLs, etc.) are also almost always caught on camera - you are unlikely to be stopped by an authority - and the fines issued by mail, sometimes months after the trip. Download the free Ebook "Driving in Italy" for boning up in advance.

https://italybeyondtheobvious.com/blog/

As well, you'd want to make sure nothing that you do not want to lose, such as your luggage, is in plain sight in your car if you leave it unattended.

For trains in Italy, point-to-point tickets are almost always better than a pass, Eurail (there is no "Eurorail") or otherwise. As the others have said, if your travels take you largely to places the trains go, I'd choose rail over road, hand's down. If going to out-of-the way places, then maybe rent a car for a couple of days. Make sure that everyone who will be driving gets an international driving permit (IDP) before the trip.

Eurail passes are not convenient in Spain, France and Italy due to mandatory reservations that cannot even be made online in the case of Spain. Point-to-point tickets are the way to go!

Returning rental a car to a different country will incur a large drop off fee. We were quoted a 1000Euro drop fee ,Portugal to Spain so took a taxi over the border and picked up a Spanish rental car.

Suki, I'm pretty sure with leasing you can overcome that obstacle, but of course we have no idea how long lcduncan is going to be traveling.
https://www.autoeurope.com/short-term-car-lease-europe/
Good to know for those lucky enough to be traveling more than 20 days!

A one-way rental from Spain to Italy will incur a 'drop' fee of $990-$2K+ depending on the vehicle class/size.

That seems to make rail the default choice. Or multiple rentals; one per country, to minimize the drop fees. Intra-country drop fees are less than Inter-country, but seem to have become more common than in the past, where it was unusual.

I am surprised that there is so little known about the French Government short-term leasing program vs renting a vehicle. The big decider is how long you will be using the car, and if you can live with the limited pick-up / drop-off points. I believe it's something like 19 days and longer will make the price better than renting, but there are numerous other included benefits that have made this an attractive option for European touring. I am scheduled for my 5th lease in Mid-May for a tour of Germany, and even the new 49-Euro monthly German transit pass is going to give me pause on utilizing the lease.

Take a "trial booking" on https://www.motorvana.com/car-lease/europe/short-term/citroen-renault-peugeot-tax-free (one of several leasing sites, and check the price for your journey. The listed advantages of the lease program are numerous, but the full insurance weighs heavily on my peace of mind. A new, factory delivered car is guaranteed, as opposed to "Well, this is the only car we currently have available that was returned today" common situation with rentals. And driving in Europe is very much the same as driving in the US. Pay attention to the posted speed limits and park according to the rules. I can brag that I have logged around 10,000 miles in Europe and have had no speeding tickets or parking tickets, although I always hold my breath for 2-3 months after trips in case I messed-up. The parking in cities can run up to 20 Euros/day, but I consider the advantage of the freedom of travel a luxury well worth the peace of mind. Quite frankly, over the several trips, we feel the smaller cities more enjoyable than the big cities.
Sorry to run on, but you probably get that I'm sold on the leasing. Note that the hidden luggage volume of the car is important when selecting the vehicle you will get, again as opposed as to the "possible" volume of the rental vehicle that you "may" get. That is important when you are more than just a couple traveling together.