When using metal nanoparticles with SPR ,the absorption , scattering and fluorescence properties can be used for biosensing.The Nanomaterials bound with biomolecule and label them.These Nanomaterials don't have photobleaching properties like other dyes.
SPR is the "gold standard" for label-free measurements. It has the largest market share and a huge community (i.e. references, protocols...). Besides other technical advantages - as mentioned before they are definitely dependent on the application - in my opinion the main advantage is that it is the most established technology.
As Shavkat mentions, it is difficult to stipulate the advantages without knowing the application. Martin makes an important point- SPR is a far more refined technology than LSPR and subsequently there are many more commercial SPR systems.
I provide a link to a review on LSPR biosensors I wrote- focusing on their prospects as a low-cost biosensing platform, hopefully you may find it interesting. There is a massive divide between academia and the commercial sectors and this is important to acknowledge. I refer to many review papers that should also be useful in answering your question.
Kindest regards,
Jules
http://www.mdpi.com/2079-6374/4/2/172
Article Localized Surface Plasmon Resonance as a Biosensing Platform...