Are there any disadvantages to pre-ordering the latest iPhone through Apple? I hope to upgrade replace my existing iPhone with the new iPhone by pre-ordering through Apple, but I'm uncertain what effect this will have on my existing data plan. 

Are there any advantages to purchasing the phone through my carrier instead? Will I be given different service options, or will different features be available?
If you're specifically asking if you can maintain your current data plan when ordering via Apple, you can do that.  Alternatively, you'll also be able to change your data plan to other plans that are currently offered by your carrier.

Part of the ordering process (when ordering through anyone: Apple, a carrier, Best Buy, etc.) is selecting your plan, and that part of the process contacts your carrier's systems.  On the first day people can preorder, this results in the carriers' systems being crushed due to all the demand.

Once your carrier's system has been contacted, the store you're buying from then knows if you're eligible for subsidized contract pricing or if you'll have to pay unsubsidized pricing.  The store also knows your current plan, and so is able to offer that as an option if you have a grandfathered plan that isn't available to new subscribers.

Ergo, the process for buying an iPhone will be pretty similar no matter where you buy it from.  Pick a store based on whatever criteria you wish: availability of the specific model you want, convenience of store location, store loyalty plan, etc.