What are the advantages of my ISP holding my external DNS instead of my firm having its own external DNS in my DMZ zone?

It depends on your experience with DNS and Networking, but implementation and service levels should also be considered.

Advantages of ISP Hosting:

1. Hardware costs (i.e. you don't pay them)

If your DNS Hosting costs you £100 a year, but a server costs £1000 it will take 10 years to justify the investment in purely physical terms.

2. Network Security

Public DNS Servers have a few "should not's", here are a couple:

Should not allow Recursive Queries (resolve for domain names other than those it is authoritative for).

Should not host private zones (such as Active Directory zones).

3. Redundancy

To maintain service Public DNS Servers should not rely on a single physical network (Internet) connection.

Multiple DNS Servers should be used. If the first cannot be done, the two servers should be on separate internet connections.


Advantages of Local Hosting:

1. Changes are easy

You can change it locally, you have direct control of the TTL, etc, etc.

2. No restrictions on record types

Many ISPs, especially those with web-interfaces for DNS, restrict the record types you can create.

HTH

Chris

Sure. It's generally the reverse of the advantages for the other option (if you see what I mean).

So, for local hosting we could consider the disadvantages to be:

Everything is your responsibility:
 - Network Security
 - Server Security
 - Zone consistency (or prevention of errors in zones)

And the costs if you're doing it properly:
 - Redundancy
 - Service Levels

And for ISP Hosting the disadvantages are:

Lack of flexibility:
 - Record Types
 - Ease of Update
 - TTL

Bear in mind that the impact of each depends on the scale you want this to run on. If you don't mind a single server, on a single network connection, and your business won't yell at you if either drops the costs are substantially reduced.

If the business considers its web-page, e-mail services to be fundamentally important then hosting DNS without redundancy and fault tolerance is not wise.

Chris