I'm in a situation where I'm going to deploy a small database to a server. It can easily run in the confines of SQL Server 2008 Express. However, I could also, if I wish, deploy this to SQL Server 2008 Enterprise.
Assuming that Express has all the functionality and size that I need. Does it offer any speed advantage over Enterprise? i.e. given that both will be sufficient for my needs which would be better to use?
SQL Server Express is free... You can always consider an upgrade if your app grows larger than you expected.
Express can only use 1 CPU & 1GB of RAM which could definitely effect performance in the wild if you are not sure how your app's utilization will be.
It also doesn't come with SQL Agent or SQL Profiler.
If this seems to be too limiting then I would consider Enterprise.
Assuming that Express has all the functionality and size that I need
Seems like you've answered your own question. The most cost effective thing would be to use Express until you approach its limits. At that point, you don't necessarily have to go all the way up to Enterprise. Workgroup or Standard Edition might be more reasonable, depending on your requirements.
See http://www.microsoft.com/sqlserver/2008/en/us/editions-compare.aspx for extensive information about the differences of the editions.