Avoiding "gmail" (external email provider) provides:
- Better privacy protection
Avoiding gmail removes unnecessary sending and receiving hop inside NSA.gov(.us) country in gmail case
- Better trouble shouting
Debugging delivery problems is simpler in email server under your admins control
IMHO: Using own email server is a good choice for most companies except mostly (very) small ones. Running email server is pretty cheap for medium size companies. "Gmail" (external email provider) may be a better choice when semi competent email postmaster skills are unavailable at acceptable price and privacy expectations are moderate or less.
It is not "one choice fits everyone" situation.