|I've heard that Border Collies are sensitive to some kinds of anesthesia. Is this true?|
There are several factors that are not explicit in this statement.
1) This is not necessarily fact. It could be, but there has been no scientific study that demonstrates this sensitivity clearly.
2) There are alternatives to using barbituate based anesthetics that are equally safe, if not safer. (Mainly Isofluorane)
3) Some vets are more comfortable using their "tried and true" practice for anesthesia, making it riskier to employ different, less familiar protocols
4) Many BC breeders and owners have noted and reported the sensitivity to barbituates
5) Done properly, even sensitive dogs can be successfully anesthetized with barbituate-based drugs.
6) Isofluorane is more expensive than the barbituate-based ones and requires newer technologies. Isofluorane does not put the dog as far "under" and recovery is much quicker (and hence, safer).
My feeling is this: why risk the possible sensitivity if you don't have to? - but only if your vet feels comfortable doing it. You need to weigh all the above mentioned factors, in discussion with your vet, and see which way the balance tips for you.