April 2019 or September 2019?

I have done both, April (and May) and September. Both times weather was great. A little more moisture in April/May but the highest rainfall day I had ever had in Italy was in September at Vernazza, oddly.

I like the spring over the fall. The atmosphere is less hazy and the colors more pronounced. Fall seemed to bring a general haze to the countryside and it affected my photography. However, I would go to Italy anytime, except perhaps August.

I find the shortening of daylight hours becomes pretty noticeable as you move through the month of September. I'm a sunlight person, so it bugs me to be traveling then. For most people it's not an issue at all.

April definitely...unless you are going to northern Italy especially the Dolomites because it is too cold

I love Italy in September. Too me April can be iffy weather-wise.

I've been to Italy (all north of Rome) in May & September, 3 weeks each trip. I preferred September. The weather was better and there was plenty of sunlight for me.

What is best for you may not be best for someone else.

In terms of daylight hours and the time of sunset, April 5 is exactly the same as Sept 4. So if we are comparing both months at the beginning, there is no difference. But as you advance later in the month, in September days get shorter, while in April they get longer. So at the end of April the sun sets over one hour later compared to the end of September.

In terms of temperatures, September is significantly warmer than April, any time of the month, but especially at the beginning of the month; early September is hot, in the 80s F, while in early April it is still cool, especially at night (it may even snow at low altitudes sometimes).

Rainfall is generally a higher in September in terms of total millimeters. However in September that are generally fewer rain days compared to April. Moral of the story, there are fewer rainy days in September, but when it does rain, it can be a short lived major downpour of cats and dogs.

You tell me what is best.

September, in my opinion, is the best time to travel.

September for north of Florence.
April for south of Florence.

We have been to Italy in September (Tuscany, Umbria, Southern Italy and Sicily). The weather was beautiful.

Not only would I expect September to be significantly hotter than April, I would expect significantly more tourists in September - except for around Easter, though next year it's April 21 so mid-month . . . .

I will add that March is generally pleasant weather and significantly cheaper room rates. On the other hand, if the Cinque Terre is a high priority (it wouldn't be for me), then maybe September is best.

September is not really variable - it's still warm. It's also busy - not really shoulder season yet.

As you see, everyone has a different standard for "best" weather. So you should look at Wunderground for historical data, rather than relying on other people's impressions. For instance, here's a direct link to the weather on April 11, 2017 in Rome. Play around with other dates and other cities to get a more rounded impression. https://www.wunderground.com/history/airport/LIRU/2017/4/11/DailyHistory.html?req_city=&req_state=&req_statename=&reqdb.zip=&reqdb.magic=&reqdb.wmo=

I think Sept will be more crowded than April with the BIG exception of right around Easter.

April much more likely to rain

Sept going to be warmer. Great for Cinque Terre and you could swim in the water. April no swimming and overall not as good for Cinque Terre but I think better for Rome where Sept is usually hot. Late Sept Rome would be better than Early sept. so if going then work your way down south and if going in April work your way north.

April better for the scenery in Tuscany. More green.

Overall I would vote for Sept due to the rain factor and is nice to be able to take a dip if going to Cinque Terre. If you are very crowd adverse though April as long as avoiding Easter you may prefer.

We went in March. Only had 1 day of rain. Low crowds and lower prices. I would go back during this time.

April 2019 is Easter time. Honestly, I would avoid that :) September (especially second half) shouldn't be too hot. Well, you can never know one year in advance how the weather will treat you, but should be fine.
September offers lots of seasonal experiences in Italy like grape harvest, swimming in the lakes (check out Lake Garda, it's gorgeous!), and you might consider eating more of gelato than in April (our tour group ate kilos of ice cream last year..).
April has its perks too, but, well, the weather is less stable.
Whenever you go, I'm sure you fall in love with Italy :)