I went on aaa.com and put in my dates and the rates are the same as going direct through Universal
Like everything with hotel reservations, it does depend on when you're going, how long you're staying, and when you book your trip. The website that has the best rates this week may not be the one that has the best rates next week.
I don't know which hotel you were considering (since you were talking about going through Universal, I assume you mean you're staying onsite), but I found these prices (per night, for the cheapest available room) on popular travel sites for April 12-17, using Royal Pacific as an example:
Royal Pacific:
Cheaptickets (w/ code): $163
Universal / Loews: $202
AAA: $202
Last Minute Travel: $206
For your dates, it's clearly cheaper to book through Cheaptickets with their current promo code, or to call Loews directly and see if they'll price match (which they should).
I'm interested in early June (Sunday-Friday, like your trip):
AAA: $166
Cheaptickets (w/ code): $204
Universal / Loews: $258
Last Minute Travel: $N/A
So, for my trip, I'm better off with AAA.
Note that Last Minute Travel didn't have the Royal Pacific available during my week, but they did have it during yours - and it wasn't as good as the regular UO/Loews rate.
There might be a better APH rate as well, but I couldn't pull one up for either rate. APH rates are apparently added in 3-6 months out, so those rates could eventually be better than any of these.
Note that you're never getting the best deal via the UO or Loew's website, at least not without calling them and asking for a price match.