It's quite different. Both functionally and, in some states, legally.
Functionally - kipfoot broke it out pretty nicely. They are your client. They hired you. Their ability to take criticism of their work is likely going to be much more limited than the other way around. After all, they are not beholden to you. You are beholden to them. If they decide they don't like working with you, they go find another engineer and you're left without work. If the same thing happened with a freelancer, you haven't lost any work. Sure, finding a replacement might be a hassle, but at least you're not trying to find a new one while also not having work to do.
Architectural drafting and structural drafting are NOT the same. Sure, you use the same tools, but the way things are shown are quite different. Attempting to retrain an architectural draftsman to show it correctly will be a pain. And assuming it works, you'll have limited return on your investment. You'll only be able to use that person when you're doing jobs with that client and you get that draftsman. So you may end up having to 'train' 5 or 6 people rather than one or two (or none, if you find an experienced structural drafter to work with), or just providing your CAD standard to a drafting firm and leaning on their managers to train and enforce your written standard.
Legally, it matters in some places. Here, for instance, I can't seal anything that is produced by somebody who is not an employee of or contractor hired by the firm that I work for. That means the architectural firm would have to be under contract to me, but that's not how it works on any of my projects. They are prime and I'm under contract to them. I imagine having two contracts in place would be a bit of a mess and make for a bit of a legal quagmire if anything ever went bad.