Adobe says LR uses an "adaptive hybrid of bicubic smoother and bicubic sharper" in export for down sizing. My own experience suggests that leaving it to LR to decide is pretty good but I can see the difference when I have more control of the method as when using PhotoShop CS6 compared to LR 4.3. My workflow is to import with LR due to its very good library function. When evaluating the files, the decision is made as to whether an image deserves more care and control than is possible in LR. All the rest are processed in LR as needed. The ones marked for more serious post are exported to Photoshop or Nikon Capture NX2. The biggest advantage when using NX2 is you start with a RAW file rendered the way the camera would render a JPG, which is often a very good starting point. Rendering is done in NX2 and 16bit TIFF's are made to be imported to PS for Adobe's very good print quality. If an image is going to get a lot of pixel level editing I just open in PS to start with. I believe I am getting better rendering in NX2 and better printing from PS, and getting the most intuitive, easiest adjustments in LR for the majority.
Edit: I forgot one step that makes a difference. In export of Lightroom, you are given a choice of maximum file size. Make sure that box is not checked because the value heavily impacts the resizing method. Set your image size but not the file size. Also, there is some confusion about the resolution box. That does not change the image file at all, that embeds the entered value in the print defaults, which you can change at the time of printing. Leaving the quality slider at some point over 60% and under 100% has little visual impact on the screen appearance so if file size is of concern set it up around 65-75% for the smallest file that shows very little artifacts from compression. Below 60 or so, you will see a negative impact, along with smaller file size. Stan St Petersburg Russia