Does it make any difference which provider I get my SSL/TLS certificate from? In particular, what are the pros and cons getting an SSL certificate from Verisign vs getting one from Thawte? Which one can be used on more devices?
According to Verisign, it is best to buy your certificates from Verisign, because then the obtention fee goes into Verisign's pocket, and not Thawte's pocket. Understandingly, Thawte's point of view somewhat differs.
Since they both comply to the same standard (X.509), there's no problem in using a certificate from either in any kind of device. What could make a CA a better choice than any other is:
In practice, Verisign and Thawte are quite on par with each other for all these criteria, so you may choose the one which has the Web site colours which please you most, or whatever. If you really must make a choice, it won't be technical, rather legal: which one offers the best financial guarantees if a mishap occurs ? See with your legal department, then.