In a side by side comparison, they are pretty much identical.
The RTIC is a 1/4" taller, but overall they are extremely similar.
The diameter is pretty much identical and the lids are actually easily interchanged. The RTIC does have a little different slot to drink out of as they have added a hole to better allow a straw. Other than that there is no real difference. Having had both tumblers since their release, I can honestly say I don't notice a difference other than the price. In the initial purchase we dropped roughly $35 (though now they are insanely higher) on the YETI and $20 on the RTIC. That's a pretty solid difference. Now to really test their performance.
These were started out of the same ice water, stirred and poured the same amount, less the ice cubes. They both have a starting baseline temperature of 41.8°F. This is the basic test, the house is 71°F where the tumblers are located. Above was taken at 3:30, below was taken 4 hrs later. The result was actually a little surprising, but is testament to them both being great quality products.
Maybe in the future I will update this with a test in a higher temperature, but with the quality of both of these products, I highly doubt there would be much difference (if any) in the end result. You just have to decide which you would rather have. Do you prefer more bang for your buck, or more name for your buck?