Here’s another one I was asked about recently. It seems that they are used interchangeably to talk about a person or an animal who/which has a “compulsive preoccupation with a fixed idea or an unwanted feeling or emotion, often accompanied by symptoms of anxiety.” This is especially so when used in psychiatry, or when colloquially we talk about someone being obsessed, as explained here:
obsessive [əbˈsɛsɪv]
adj
1. (Psychiatry) Psychiatry motivated by a persistent overriding idea or impulse, often associated with anxiety and mental illness
2. continually preoccupied with a particular activity, person, or thing
Source: http://www.thefreedictionary.com/obsessive
We can find plenty of examples of both words being used to express this concept here (obsessional):
http://bnc.bl.uk/saraWeb.php?qy=obsessional&mysubmit=Go
and here (obsessive):
http://bnc.bl.uk/saraWeb.php?qy=obsessive&mysubmit=Go
http://www.thefreedictionary.com/obsessive also gives us the definition:
“Excessive in degree or nature: an obsessive need to win.”
Here I would hesitate to say an obsessional need to win. Perhaps, as with many examples, it is more about common word partnerships or collocations than about which word is more correct. Obsessive is certainly more common and to my ears sounds better in all the following, although you can find examples with obsessional as well:
An obsessive need to win // obsessive behaviour // an obsessive fascination // his or her obsessive nature // an obsessive interest // obsessive jealousy
From a learner’s point of view, I would suggest the following: use obsessive yourself and you won’t go wrong, but be aware when reading that obsessional exists as well.