The widely publicized paper Resynchronization of circadian oscillators and the east-west asymmetry of jet-lag from the journal Chaos presents a mathematical model demonstrating that the brain's "oscillatory circadian pacemaker cells" have a more difficult time adjusting after an eastward flight compared to a westward flight crossing the identical number of timezones.
The New York Times article about it is more accessible; in short ,
it would take you about eight days to recover from a westward trip across nine time zones, if you did nothing to fight it. But if you cross the same number of time zones going east, recovery would take more than 13 days, according to the model. This recovery time is worse than if you flew smack across the globe, crossing 12 time zones, which is about the distance from New York to Japan.
The lead author explains the physiology in a Travel + Leisure writeup:
“You expect to advance your internal clock if you travel east and backward if you travel west,” Girvan added. "However, if you travel a large number of time zones eastward, your internal clock doesn’t phase advance like you would expect. Instead, it phase delays.… This is what causes you to experience more severe jet lag.”
Now, this paper has not yet been followed up with empiral observations on the matter. But another highly publicized paper, Chronic Jet-Lag Increases Mortality in Aged Mice (Curr Biol. 2006 Nov 7; 16(21): R914–R916.) similarly found that
aged mice were significantly affected by light schedule changes…. At the end of the 8 week period of light schedule rotations there was 47% survival in animals whose light cycle was advanced each week, 68% in those experiencing delays of the light cycle and 83% in unshifted aged mice…. Importantly, chronic stress was not implicated in this phenomenon…. To determine whether the effects of phase advances on mortality might be related to the duration between schedule changes, mice were shifted more rapidly, every 4 days. On this schedule, advancers died faster than with weekly shifts…. Delayers fared much better than advancers….
As you may have learned from high school health class, the natural human circadian rhythm is about 24½ hours, so our body resets its "internal clock" by exposure to sunlight, so neither advancing nor delaying the cycle will be pleasant. But at least for older mice, the former is far worse for them than the latter, so you'll need to do more preparation like sleep training or have more recovery for eastbound trips than for westbound trips.