Both are great resorts and I think the post above explains both well.
Can I suggest you join a facebook page call "I was married in Fiji". Its a awesome page with ladies who are getting married or who have been married in Fiji, plus there is lots of wedding vendors such as myself who help out with information etc.
Both are really lovely, and very popular. One thing I would be checking out as well,, is if the Shangri la has a "one" wedding per day policy or if several couples can book and marry on the same day. I know the Outrigger has only one wedding per day.
Another thing to consider is the location of both with regards to other facilities for your guests. The Outrigger is a 2 minute walk along the beach to Sunset Strip, which hosts other budget hotels such as the Bedarra Inn for your guests to consider, plus sunset strip has other restaurants for cheaper eating options.
The Outrigger is also a short 5 min drive from Sigatoka where you can grab cheaper alcohol and food/medications etc.
The Shangri La has a nicer beach and has a more private/secluded feel. But as mentioned above, the service is much better at the Outrigger.
Congrats on your upcoming wedding and happy organising