Can the Raspberry Pi B+ run Kodi efficiently or should I get the Raspberry Pi 3?
I've had various flavours of pi tucked behind my tv running kodi for years now, upgrading whenever a new model turns up. The biggest differences you're likely to notice moving between the pi A/B -> A+/B+ -> pi 2 -> pi 3 are the performance of the graphics (faster, slicker menus), and the performance of the scraping system. The scraping part is a much bigger deal. When you're dealing with fairly large libraries it can get you down waiting the best part of a day for the first pass at identifying all your files. Adding more library content and waiting for it to be scraped, added to your database, and the changes propagated to clients like yatse, is boring. Later models reduce this significantly.
Streaming performance is fine on lower end models, but I'd strongly recommend at least a pi 2 just for the usability bump.
I have Kodi running (as part of OpenELEC) on a Raspberry Pi model B (not the +) and it does just fine, including playing Blue-Ray videos over the network. So the answer is: yes, it will run fine - however, if you install Kodi on a "normal" raspbian installation there is more overhead than running it as part of the immensely tuned OpenELEC.
I know this post is about a year old now but for anyone else stumbling across: i'm running kodi on xbian on my pi b+ and it runs ok but its nowhere near smooth. Loading and menu building times are an issue and if you've got a boy-/girlfriend sitting next to you who is used to watching online streams on a laptop or pc you will have to deal with some criticism x) better get a newer model as suggested and please double check any devices bought on ebay, as that is how i ended up with a model b+ instead of 2b.