Train from Basel to Milan

For what date, and where are you seeing those prices? That gap does seem wider than usual.

I've never found anything wrong with 2nd class on main-line trains.

Leaves and arrives at exactly the same time. I only travel 1st class if the cost is 10 EUR (or CHF) more.
I just looked at Trenitalia.com for June 7, at 6:31. For the first leg, Basel to Milan, the full fare is 102 EUR, but there is a MiniFare of 49 EUR is available in 1st class. The second leg, Milan to Florence, has 4 classes of service, Standard, Premium, Business, Executive. There is an Economy Standard fare of 39.90 available. So you could get a nonrefundable ticket for 88.90 EUR. I checked the SBB site and they are selling a nonrefundable ticket on the same trains for 102 CHF.

A full fare ticket in 1st/Executive class would be 164 EUR plus 131 EUR totally 295 EUR.

In short, ticket prices are all over the place because of the various availability or nonavailability of discount ticket tranches and whether tickets are full fare or discounted, nonrefundable.

I don't know where you are looking, but with prices in '$' (is that Canadian, Australian or what?) you are obviously not looking at either the SBB or Trenitalia websites.
I would use SBB, because Trenitalia, does not do Swiss internal trains, and most of the trains from Basel to Milan involve a change somewhere in Switzerland.

I just looked on SBB ( http://www.sbb.ch/en/home.html ) for a random date in late April, and it quoted me CHF 93 2nd class, CHF 161 1st class. 50-60% surcharge for first class is about normal.

First class gets you 2+1 seating instead of 2+2, and proportionality more legroom, so you are paying for 50% more space on the train, nothing else. I would not pay that much extra for first class, there is plenty of room in 2nd class.