I'm debating buying a mac mini with the regular client OS or the model with the server os for the purposes of replacing my home server. Are there any advantages for such a use with the server os?
There are advantages and disadvantages, of course. Should you buy the server version? As always, the answer is, "it depends." Do you need to run any of the following?
Most or all of these features are available in free, open source products (in fact, many of them are based on the open source projects). You can add OpenLDAP, OpenVPN, Apache, Samba, Calendar Server, etc. to a client Mac OS X installation if you want. However, Mac OS X Server wraps them up into a nice, aesthetic, easy-to-administer package. This could be a net positive or negative to you depending on what you want from this machine.
By purchasing a Mac mini server, the extra hard drive is nice but you sacrifice the DVD drive. This might be a deal breaker depending on what else you plan to use this home server for. You can always add an external one, but that is extra cost and hassle. Again, it's a trade-off.
Without knowing what you use your current server for, the client OS Mini may fit all your necessary needs.
wikipedia lists the features of the server OS. I know that some of these can be added to the client version if necessary. Also the clientOS Mini comes with iLife.
I use mine(clientOS model) as a media storage/server with a couple of large disks running in a firewire 800 enclosure, which fits my needs nicely.