It seems it will be the F-35, but I’m not completely sure.
Both teams still have time in their current platforms, but one more so than the other.
Navy practice is to give the Blues the oldest possible Hornets that are still flyable, working under the idea that the earlier the jet, the lighter it is. Lighter jet, better airshow performer.
The Thunderbirds are in the Block 52 variant of the F-16C, and the last of these were delivered to the team as new-build jets in 2008 after having the modifications done that they need. The Block 52 is the last F-16 variant that the USAF is buying. A new F-16 in 2008 can likely fly around 15-20,000 flight hours before it is considered too old to soldier on. Add to this equation that both teams logged significantly less flight time in 2013 thanks to the budget fight, and the jets likely got almost another year added to their lives. In theory, the Air Force could rotate other Block 52’s in as they get pushed out of combat units. That process would theoretically last until it was no longer cost-effective to keep the Block 52 flying.
As to what’s next, I can’t see the United States transitioning away from a frontline fighter for the demo teams. The teams are ambassadors and recruiting tools extraordinaire, and that mission does not get accomplished if the hotshots who fly for public demo are not flying the baddest and best tactical fighter platforms available for their respective services. The United States is the only nation that I’m aware of that uses frontline combat aircraft for their multi-ship demo teams. The only exception to this rule came from the oil crisis of the late 70’s when the Thunderbirds flew T-38 Talons. I think the Blues kept their F-4’s during this time, but I can’t remember offhand if they were F-4E or F-4J.
Long story short, Super Hornets and progressively older -16’s. Once the F-16 is retired, there is only the F-35 since the F-22 is too powerful with the thrust vectoring and supercruise capabilities.