I've just finished the Animal Behaviour and Welfare degree at Bristol, and have plenty of Zoology friends so hopefully can help. Despite sounding similar the degrees are very very different in years 2 and 3. Both have a common biology first year, where all biological scientists (bio/zoo/botany etc etc) are together and have to do 2 compulsory biology modules. After this however, the courses are rather different.
-Animal Behaviour and Welfare is based in the research group out at Langford (the vet school) 30 mins from Bristol, where Zoology is in the school of biological sciences on the main campus.
-Zoology is more fundamental biology, and is concerned mainly with wild animals behaviour in a more evoultionary context. ABW is more concerned with domestic animals (farm, companion animals etc.) and is a whole discipline of its own. As it is fairly new, it is less known so people have preconceived ideas that it is less academic or respectable, but I am sure its reputation will raise in time. I'm going straight from it to a PhD in October, and hopefully a career in research so it certainly can be academic!
-Animal Behaviour in zoology is very limited to one or two modules, and is concentrated mainly around a few wild animals and insects (lots on ant behaviour if thats your thing!). This is in quite a fundamental setting, and despite the word 'zoo', is not very much to do with zoos, and at times, not much to do with what you would think of as animals (insects, bacteria etc.) (I'm sure you weren't thinking that but some people are definitely surprised!)
-ABW obviously has the element of welfare in it (1/3rd of the 1st year and 1/6th of the 3rd year). Much of the behaviour is also in the context of animal welfare---so evidently having an interest in animal welfare is very important!
The course is also more practical in the sense of around 20 day long visits to animal related instituations (farms, research centres, shelters etc) in 2nd year, and further vists and a 40 credit practical dissertation in third year. In zoology there is no dissertation as such, instead a smaller library and lab based project.
Obviously I'm very biased to ABW, as this is where my research interests lie- but I just thought I would emphasise the differences in these degrees which on the surface appear similar but really are very different. You can apply for both via UCAS, but would encourage you to go to the open days for both, speak to staff/pupils and get a real feel for the courses before deciding!