gmail vs yahoo mail

Neither.

If you want to take your business serious and have it look professional, you don't use gmail, yahoo, hotmail or such kind of email address. You register your own business domain and use an email addres from that business domain.
There are lots of company's which won't take your company serious if you're using gmail as company email.

As for private pruposes, ofcourse Gmail, because you can also use that in an email client and not only via webmail like yahoo.