It's hard to say for sure. Memphis is/was surely a redundant hub in the Delta system.
I could see more service to the south central part of the US from SLC. Delta has recently added more service from SLC to Houston, Dallas, Austin, and San Antonio. I wouldn't be surprised to see the nonstop to Little Rock come back (it ended around 2008 or 2009 but did relatively well). Otherwise, I don't predict a whole lot of change locally as a result of the Memphis hub closing.
On a side note...the airport is having regular meetings now with the achitecture firm assigned to design the new terminal (HOK), and airport tenants (with Delta on the designing board). Minor changes are made at each meeting. The airport is getting busier for the summer season. The SLC-Paris route was upgraded to an Airbus 330 for the summer months adding more seats and a better performing and larger aircraft than previous summers. The US Airways SLC to Philadelphia route started yesterday and flights so far have been full.
Our airport is oftenly the first and last impression we leave upon visitors to our city and even the only impression (millions of passengers fly through SLC every year just to connect flights. We can easily persuade a lot of these people to come visit longer). I will say, there are so many passengers who awe at the scenery just seen from the windows in the concourses and the intrigue the area gives. Again, I encourage everyone to submit your feedback on what you want to see in the new terminal at
www.myairportslc.com.