Which is best for me - Email marketing software or an Email marketing service?

By using either of them you can be sure of getting a great deal that will quickly pay you back in increased sales and improved customer relationships.
If you already have marketing staff then putting them to work on specialized Email marketing software makes sense.
Or, if you employ an Email marketing service, you only need a web-browser to get started. All you need to do is contact the service provider over the internet and let them get on with it. This is a really good idea if you have a small company; rather than over-stretching your existing staff, you can simply get someone else to produce the email marketing material.