Advantages and disadvantages of using an external wiki over an internal hosted one

Advantages of an external wiki over an internal one

Which you choose depends on how you're using the wiki: If the whole of the course taking place in the wiki it's a VLE in itself. And an external one might give you enough flexibility.
Supported in-house by IT department - they may be able to add or limit features as you require - they can also cause time delays that don't meet the needs of academics or students.
Possiblity of internal failiure - how good are college or universitiy back up protocols (having been stung on at least 4 occassions when back up procedures have failed)
External wikis have the ability to stay very up to date and to improve on a monthly (or even weekly) basis
Ownership issues seem to be resolved - Academics and students in one instituion have fed back that they feel an external wiki is theirs while an internal one is the University's (Seems illogical but perceptions often are.)

You may have space limitations (but you could always create more than 1 wiki and then link them together)
Possibility of external tech failure (like when educspaces announced it was closing in the middle of people's blogging-based courses - luckily it was saved, but it's a message! - the need to look for systems with well funded support)
Which you choose depends on how you're using the wiki - if is it just a small part of a course using technology it may sit naturally within the institutional VLE and the wiki available within that
The provider may start charging for the use of the service
There may be some issues of confidentiality - if students are working on something that is case study based.
There may be issues of IPR, most wikis invest some of the IPR in the provider.