The two degree courses vary hugely between different universities. At most unis, they are pretty much one and the same. Zoology degrees aren't really just 'the study of animals'- they are just a selection of particular biology modules, including development (animal and plant), molecular etc. It really does depend on the uni as to what modules are included.
For what it's worth, my undergrad was zoology- I then went into conservation research, PhD etc with no problems. Those students on different routes (biology, ecology, molecular etc) studied pretty much exactly the same modules for the first year, mostly the same for second year, and a bit more varied in third year. A few years ago my uni changed the naming of their degrees, so that all the routes are called 'biological sciences', including the exact undergrad I did (same modules etc). The idea behind it was to make it simpler and allow more flexibility. A lot of unis have done the same. The title really is pretty meaningless!
Basically, if you're worried about the content of the degrees, don't be- look at the course specification as the title tells you nothing about what is included.
If you're worried about what employers etc will think, also don't be. Any employer worth their salt (especially if they are science related!) will understand that the two routes are equivalent. She'll probably have a few idiots asking her if she wants to be a zookeeper at some point, but it's generally just kids that think that.
In terms of her future, the uni she goes to is more important than the exact content of her degree. Any degree in biological sciences will stand her in good stead to do a masters, PhD, research, work in science etc. It is assumed that if you have a good degree you also have the capacity to learn what you need to learn (assuming a good grounding in basic principles, which you'd get from any bioscience degree). Check the league tables- Cambridge, Oxford, Durham, UCL, Imperial are all excellent, for example.
Don't put her off zoology- it's not the joke degree some people think it is! It really is just the same as 'biological sciences' and anyone remotely in the field knows that. Let her make the choice based on which uni and course suits her best- the course name on the certificate at the end doesn't matter. (The classification does though!)