Already answered ("no"), in particular Rick's most recent posting goes straight to the core of the matter "Physics is immutable. A heavier bullet is longer and has a higher B.C. and will loose velocity and energy at a slower rate than a lighter 1 will"
Another factor too, the .408 CheyTac is proportionately a bit smaller of a cartridge than the .50BMG is. The normalized case volume:bore size for the .408 is ".308-class", the .50BMG is ".30-06 class". This isn't a big difference, but basically the .50BMG is about 10% more "overbore" than the .408 is. That won't give the .50 a 10% more muzzle velocity boost, but it will be worth 4-6% (the same velocity edge that a .30-06 has over a .308 Win).
To that you have to multiply by the ratio of the calibres, which is roughly 5/4. So the .50BMG will gain about 25% over the .408 simply by virtue of it being 25% bigger.
All other things being equal (chamber pressure, barrel length in "calibres", rifle accuracy, bullet technology leve,l and bullet weight and length in proportion to bore size), the 50BMG will outperform the .408 by about 30%.