Provence in month of May -- should I base in Avignon or Aix en Provence?

I don't know Aix, however we had four nights in Avignon (arriving by train) and we loved it, with some good day-trip options available. And the Palais des Papes in town is superb. We also took local buses (not a tour) to Les Baux and Arles and back ... great day.

Both are easily accessible by train.
We have always been there with our own car but what do you mean by 'tours'? Is that organised tours or visiting places on your own with public transportation?
Avignon is fine but as a place to stay i like Aix more as the quintessential Provençal town. Conveniency for day trips will also depend on where you'd like going. There certainly are possibilities out of Aix.
http://travel.aixenprovencetourism.com/en/itineraries-and-packages/suggested-itineraries/discovery-tour/
http://www.aixenprovencetourism.com/en/go/getting-around/public-transport-networks/
I am aware that Avignon might offer more connections since it is bigger, but then again it depends on the time you have and what/how much you can do with it.

I regret not including Aix, notwithstanding how much we enjoyed Avignon ... can you split your time between them OP? There were tours available ex Avignon - dozens in fact - but I would always check that a public bus can't get you there.

The trains between both places run more frequently compared to the bus.
Rsmokester, how many days are a few days, and how many days would you have for day trips?

I wasn't referring to travel between the two - I'm talking about local buses to nearby attractions - small villages that are too cute, wineries, Roman ruins, lavender farms ... that sort of thing.

A few years ago I used Aix-en-Provence as a base and made day trips to nearby towns and villages, using regional busses, €1 a ride. The area is associated with Cezanne and Picasso.

Well, both Avignone and Aix are very beautiful. They are very different from one another, but they are both worth a visit. If you are going to visit Luberon, Fontaine de Vaulcuse, Arles, Orange, Nimes - Avignone is more confortable. From Aix en Provence is easier to reach & visit Marsiglia or Calanques.

If you have a look into Google for "tour operators Avignon", or Aix, you will find a big choice. And in both towns the tourism offices people are kind and very helpful too.

Thanks for the mentioning the Pope's Palace. That's a good thing to keep in mind for Avignon. Hadn't thought of taking local buses around Provence. That's a good idea fro a more DIY approach.