This depends a lot on the provider too. There have been instances when I did not receive mails to my yahoo account because their mta is blocking my friend's email. But generally, the biggest advantage is about using your own domainname in your contact. If your provider is good, there will be no issues at all.
A lot of the issues get corrected quickly because shared mail server issues are reported early as it affects a lot of users.
I think it should be pointed out some very strange things have been happening regarding email....which should add to your concern. Earthlink's email servers were taken down *again* last night for a monsterous 6 hour period. This, in itself, tells you something very big is happening...they did this last week too.
I have a main email relay point...and have noticed relay times have begun to be crazy. Really, really crazy. Try 3 hours. I have never seen anything like that...and had only started noticing it last week.
I have no explainations. Email is far from secure or reliable. There is no way you can have two email servers receive email for the same exact address. The only think I know to do is to have two or three primary email addresses..and have relays setup..and monitor those relay times.