If your university or department specifies a preferred referencing style, use it. Or if you're submitting a paper for publication, follow their submission guidelines. But if you have the freedom to choose a referencing style, I would go for numbered references.

Some sentences or paragraphs may have several references associated with them. This can get very cumbersome if you list every author and date. For example;

Since the invention of scanning probe microscopy techniques in the 1980s [Binning, G. & Rohrer, H., 1981, Binnig, G., Quate, C.F. & Gerber, Ch.,1986], there has been a concerted effort to extend their functionality beyond imaging. This includes manipulation of individual atoms on surfaces [Stroscio, J. A. & Eigler, D. M., 1991]...

Almost half the paragraph here is taken up by bibliographic information, and it would be worse if the papers cited had more authors. This breaks up the flow of the text and makes it hard to read, even with only three references.

Also, if the reader wants to look up all of these articles - listed alphabetically in the bibliography - the first two references will be under "B", the third under "S".This means extra work hunting around in the bibliography for the right paper, trying to remember the names of the first authors of all the papers listed. This gets even more complicated if you cite many papers by the same authors.

But if we use numbered references...  

Since the invention of scanning probe microscopy techniques in the 1980s [1,2], there has been a concerted effort to extend their functionality beyond imaging. This includes manipulation of individual atoms on surfaces [3]...

The text is much easier to read. and the references will be grouped together in the bibliography. It's much easier to remember "1-3", than "Binnig & Rohrer 1981, Binnig, Quate & Gerber 1986, Stroscio & Eigler 1991".