I'm not sure if you just want to match two images (e.g. find the common points), or you want to attempt something like CBIR (Content-based image retrieval -- searching a database with a template image to find all that contain the object).
I am currently doing CBIR research, so I am pretty up-to-date with current methods. Here and here are the links to my answers to problems similar to yours from stackoverflow, you should take a look.
Now, to talk about SIFT a little bit. When if was first introduced by Lowe, the term SIFT applied both to the process of feature detection and to the feature descriptors calculated on those detected interest points. Up to this day, the SIFT descriptors have proven to be unbelievably awesome. The descriptors have some cool properties that @Totero already mentioned.
SIFT detection method, on the other hand, which is nowadays more and more referred to as DoG (Difference of Gaussians), is not state-of-the-art any more. It is still widely used, but for the process of feature detection, there are more methods today, some of which are better or nicely complement the types of invariant keypoints DoG process extracts.
Most current papers (look at the links in the linked stackoverflow questions) have one more nice practice: they combine multiple ways of detecting features, and then use SIFT descriptors (which still rock as descriptors) to calculate the invariant vector representations. I am currently working with a combination of DoG (they focus on corner-like parts of images) and MSER regions (they focus on blob-like distinguished points through multiple scales). You might want to try and experiment and throw even more type of feature detectors in there, if you find this combination not satisfactory on your particular image database.
Also, if you are interested, here is a paper that evaluates the preformances of different detection and descriptor combinations. I have not read it since DoG&MSER + SIFT works fine for me, but I've skimmed it and the paper is quite good.
PS: use google scholar if you do not have access to the IEEEXplore database I linked to.