Would it be better to take train or drive from Paris to
Monet's Gardens?
It depends on whether there are other sights you would like to see in that area. We had a car and stayed in Les Andeleys which is beautifully situated on a wide bend of the Seine and has a large ruined "King Richard" castle on the hilltop. We stayed there two nights, went to Giverny in the morning, saw Rouen sights and Honfleur the next day. There were several pretty villages north of Les Andeleys; Jumieges Abbey is also on the way to Rouen - unfortunately we didn't time that right for the ferry.
I can't say which is better, but the train is quite easy. You take the train from Gare St Lazare to Vernon. I just went in May and the roundtrip fare purchased on the day of travel was 27.80 EUR. Once you arrive in Vernon, there are buses immediately outside the station that make the drive to Monet's Garden. I think the roundtrip fare for the bus was around 8 EUR. There are a couple of other options (walking or renting a bike) as well. If you want to avoid the ticket queue at the garden, you can buy your ticket online. This site has instructions in English. If you have an advance purchased ticket, you follow the signs to the group entrance and they have an entrance for the ticket holders there.
Aside from the fabulous gardens, you can see Monet's huge murals in a special hall in the Musee de l'Orangerie. They cover entire walls. You can even take pictures if you don't use a flash.
Sylvia,, its better to take the train if just going as a daytrip from Paris. The cost of a one day rental, the hassle of driving in and out of city, the cost of making sure you refill it with gas,, and pay for parking,, why would anyone rent a car just for one day(if you were staying outside paris and spending a few days touring about like another poster did it would make a lot more sense) Buy your train ticket to Vernon, and your ticket to gardens in advance. From the train station you can rent a bike and ride to gardens ( lovely ride) or take a local bus.. easy and cheap. Tours cost a lot,, and are better suited to those who are not interested in thinking too much about how to manage a simple daytrip.. or perhaps for elderly or frail who need door to door service... for a few things they are ok ( I did a daytrip on a tour to Loire Valley, as you can't really visit Chateaus easily without renting a car and I had a child with me and didn't want to drive on my own) but I am pretty "anti tour" for most people for easy sites like Versailles or Monets Gardens.
If Giverny is your only destination for the day, take the train. Why spend all of that time picking up/returning a car when you can hop the train in a flash? Plus, you can spend more time reading or whatever since you won't be driving.
I had a look at the link provided by Alex above. He's pushing it pretty hard here in quite a few posts. It does indeed mention Giverny, but not in the sales page in the link above. If you hunt around the website it will mention it - in order to give train and car directions but not a package deal. @Alex, do you have some connection with the website you are pushing? I see that you've just changed the location in your signature from one in French.
As a solo traveler, I prefer the train for the convenience and ease of mind...no parking hassles, no worries about break-ins. I took the train from Paris last year and found it perfectly accommodating. One piece of advice; buy your tickets in advance if possible if it doesn't cost a premium. The ticket line isn't terrible and moves at a reasonable pace, but it does take away some time that you would otherwise have to head on to the gardens. Take time to enjoy the rest of the town too, not just the gardens. Have a lovely trip.