Q: IPhone 5s 16GB vs 32GB for business emails, does it make a difference?

Check your storage on your iPhone, iPad, and iPod touch - Apple Support

As with any data storing device, especially if you can't replace the hard drive, choose the most available storage capacity. If you are planing to keep your mail for an extended period of time and also get attachments like photos or other data from 3rd party apps.

And the phone will run much smoother if you don't use all the available space, plus there's more room for music, photos, videos, apps.

To check the space you use now, go to Settings/General/Storage & iCloud usage/manage usage and look for the Mail app and you'll see the amount of storage used by this or other apps on the phone.

Text emails really don't take up huge amounts of space. The sound files for your voice mail might, but, as I don't know how much, it's hard to say. Check the sound file size. Almost no one regrets buying too much memory. Lots of people regret buying too little. Buy the larger one.