This is a fantastic question! The short answer is: Mt. Everest is experiencing both uplift and erosion.

Uplift must compensate for erosion because of isostasy, which is the gravitational equilibrium of a buoyant object in a fluid or ductile medium. The easiest way to understand this is to imagine an iceberg floating in water. Because ice is only slightly less dense than water, a large “root” (~90% of the ice) is submerged beneath the water’s surface. If the part of the iceberg above water were removed, the iceberg would “bob up” and ice that was previously submerged would be above water. Also, the “root” would not extend as deeply below water.

I use the analogy of an iceberg, because the rocks at the surface of the earth follow the same principle. The lithosphere of the earth is made up of the crust and uppermost mantle that act as rigid plates (parts of the crust actually flow like silly putty instead of acting totally rigid). The lithosphere “floats” on the asthenosphere, which is the part of the upper mantle that flows sort of like an extremely viscous fluid even though it is solid (think silly putty). The figure that I have included shows the process of “isostatic adjustment” when a mountain is eroded. When the top of the mountain is removed, the system is not in isostatic equilibrium until the lithosphere “bobs up”, with the root becoming shallower. You can see that the top of the mountain in stage three is above the dashed line that marks how deeply it was eroded. This is uplift. You will also notice that the elevation of the top of the mountain after isostatic rebound is lower than in stage 1. So, while rocks were uplifted, the surface elevation actually decreased.

The model shown in the figure is simplified and doesn’t take into account lateral tectonic forces “squeezing” plates together. In the Himalaya, the Indian Plate is still moving toward the Eurasian Plate. This has cause thickening and isostatic uplift of the Tibetan Plateau and the Himalaya, but erosion is keeping pace with the uplift. If uplift were occurring without any erosion, Mount Everest would be much higher than it is. If erosion were occurring without uplift due to tectonic thickening and isostasy, Mount Everest would be much lower, like the Appalachian Mountains of eastern North America.

Mount Everest is experiencing both, uplift and erosion - but I don't know whether it is growing faster or eroding faster at this moment. Mountains that get too large also have faults that tear them apart, and I believe this may be happening to Everest as well as erosion.