Which do you prefer—April or May?

May is perfect and with a lot less tourists.
I have been in the northern part I.e. Milan in May 2018 and 2022, it was hot to me. Venice Verona Vicenza in 2018 also north it was warm. The further south the warmer the temp in Italy regardless the season.

I was just in Italy (Verona, Venice, Florence, and Rome) the last 2 weeks of March and it was crowded!! We kept saying, “I can’t imagine what this is like in the summer.” I can only imagine April and May will be even more crowded.

We had near perfect weather. It only rained once while we were inside eating dinner. It was cool in the morning (40s-50s) and warmed up in the afternoon (50s-60s).

We did find that getting out at 6:30 - 7:00 am was a great way to beat the crowds for a few hours. We found a couple of places in Rome that were not crowded in the afternoon--the Jewish Ghetto and Botanic Garden near Trastevere.

Based on historical statistics, Rome will be 50%+ rainier in April than in May, but as you note, that can vary greatly from year to year. You can review the climate-summary chart in Wikipedia's entry for Rome here: https://en.wikipedia.org/wiki/Rome That same chart shows you there's a substantially greater risk of unpleasantly hot weather in May.

The weather is to some degree unpredictable. There's an iron-clad guarantee the days will be signficantly longer in May.

To see some actual, historical, day-by-day weather data for Rome and other cities in Italy, go to the website timeanddate.com. It's most useful for temperatures.

Rome - April 2022
Rome - May 2022 (Late May got quite hot in Rome last year.)

I check five years' worth of data to get a good idea of the range of conditions to expect. Use the pull-down box just above the graph at the right to change the month and year.

You can use the Search box near the top right to check on other cities.

There is usually a surge in March and April because of spring break travel and then a little lull in May before school let's out and then the summer surge.

I don’t think crowds are significantly different between April and May. Actually if one looks at the statistical histogram in the article linked below on the number of visitors at the Uffizi Gallery in Florence in the years before and after the pandemics, it appears that May has fewer visitors than April. As a matter of fact April had the nighest number of visitors of all other months in the 3 years considered (2018, 2019, 2022).
https://www.quinewsfirenze.it/firenze-musei-da-record-ma-obiettivo-era-delocalizzare.htm

Weather wise it is hard to predict, as occasionally one has the odd year with unseasonably warm or unseasonably cool weather (I’ve been in Tuscany in the past two weeks and last week before Easter has been colder than normal), but May is likely to be warmer and less rainy than April, days are longer, everything is green, and flowers are blooming. I arrived on April 1st and on my first week I’ve been dealing with snow above 900 meters (less than 3000 ft), and deciduous plants are largely still bare. Of course things may be better in Sicily and some people may prefer temperatures below freezing, but that is not me.

So, if you ask me, May would be my choice.

I went last April first week and the crowds were insane. I’ve also traveled mid May and much preferred that though I was not in major tourist areas in my May travels and it was many years ago I was in Stresa and then Tuscany area.