From
http://www.concertpharma.com/research/#CTP499 which is found on the page from the link in your post.
"Because deuterium forms more stable bonds with carbon, deuterium substitution can in some cases alter
drug metabolism, including through improved metabolic stability, reduced formation of toxic
metabolites, increased formation of desired active metabolites, or a combination of these effects. At the
same time, because deuterium closely resembles hydrogen, the substitution of deuterium for hydrogen
has generally been found not to materially alter the intrinsic biological activity of a compound.
Deuterated compounds can generally be expected to retain biochemical potency and selectivity similar to
their hydrogen analogs."
Replacing an H with a D might turn drugs that aren't viable because they have to be injected every 2 hours/have toxic metabolites with horrible side effects into medications that can be taken orally once a day with a better safety profile then the results of taking said drug may be different, but analog to analog at equal serum levels the effects shouldn't be any different.
Maybe a deuterated analog of DMT could be taken orally without an MAO inhibitor and still be active for example(I don't know enough about MAO to venture a guess), but it shouldn't feel any different than regular DMT.