I do not think it matters.

I have used both with great success. Clay keep roots cooler but plastic retains water better.

I would say, go as big as you can. This will help with retaining moisture and keeping the roots cool in both types of containers.

Happy Gardening

Keriann~

Either one is good. Clay will dry out faster which can be good and bad. Good because you don't want the plant to stay wet too long, bad because you have to make sure it doesn't dry out completely. Plastic has the opposite effect. If it stays wet too long it will lead to rot but you don't have to water as often.

A tall plant in a plastic container will be easily knocked over on windy days whereas clay should be okay (not always).

Don't overpot your begonia. This can lead to rot because the soil doesn't dry out as fast as it needs to.

I like clay since it does dry out and doesn't keep the soil soggy. I'm fussy and baby my begonias. I fill one side of my kitchen sink with enough water so the pots can sit and soak (I alternate weak solutions of Miracle-Gro, too) the pots, then move them to drain on the empty side of the sink while I submerge the next set. So on and so on.

Here is a link that might be useful: Begonia blog