Migrating DHCP from Windows Server 2003 to Cisco PIX 506E

Moving to DHCP on the router is not normally a good idea and there are many reasons to leave DHCP where it is on the Windows Server, and noe that I can think of for moving it to the PIX.

For a start Windows Based DHCP integrates fully with Windows DNS to allow DHCP to update DNS for example.

Windows based DHCP also has a full range of DHCP options that can be set such as, sepcifying WINS servers, Domain name, NETBIOS Note type and a range of other options not normally available on router based DHCP

Keeping DHCP on the server is best idea.
Assuming that you have Active Directory, there is an issue with clients auto-registering in AD DNS on the domain controller if the DHCP server is anything other than a Windows server. Why? Because it is the DHCP servers job to register RDNS (PTR Records) for any client, and the PIX absolutely cannot do that but a Windows server can. This can cause issues with AD.
Yes, it is easy to move DHCP to the PIX, but not a good idea if you have AD.

The one thing you need to be sure of is that you don't have both online at the same time.  That's the only big thing to be certain of.  I've seen DHCP service fail for a week without anyone noticing.(Lease expiration was set to 30 days)

You can set WINS/NETBIOS Node type/Domain Name, and just about anything else on the PIX.  The 'dhcpd option' command allows for configuration of any non-standard options,

'dhcpd dns' for dns server
'dhcpd wins' for wins server
'dhcpd domain' for domain name
'dhcpd option 46 hex 0x8' for netbios node type

I'm pretty sure the default lease value for Windows DHCP server is 8 days, you can bring up DHCP admin console, look at leases, sort by expiration date and see if anyone is expiring shortly.  It really shouldn't be an issue.  I've migrated DHCP in the middle of the day many times, just make sure you force a device to retry after you migrate so you can see it pick up a lease on the new server.

The PIX actually has some DDNS options in the dhcpd config as well, although I'm not familiar with them:

'dhcpd update dns'

Dynamic DNS (DDNS) updates the name to address and address to name mappings maintained by DNS. Updates are performed in conjunction with a DHCP server. The dhcpd update dns command enables updates by the server.

Name and address mappings are contained in two types of resource records (RR):
"The A resource record contains domain name to IP address mappings.
"The PTR resource record contains IP address to domain name mappings.
DDNS updates can be used to maintain consistent information between the A and PTR RR types.