There are actually multiple issues at play here and there is no one easy answer.
For audio quality, the main issues are decoders, DACs and post-processing modes.
The decoders for the major formats (either traditional DD or DTS or the new lossless formats) should be the same whether they are in the receiver or in the player. As long as the player has all the decoders, simply from the decoding perspective, it really should not matter where the decoding happens. One nuance is that on BR discs there is a secondary audio stream - typically for commentary during the movie. That secondary audio stream can only be accessed when using the decoder in the player.
Once the audio signal is decoded it needs to be converted to analog for playing. The only way to send the lossless digital signals is through HDMI. For the digital to audio conversion, one main issue is the quality of the DACs and associated electronics. Some BR players (like the higher end Pioneer and Denon players) have been optimzed for their analog performance. Many entry level ones have not - they assume HDMI will be used. In any case, you need to compare the D to A conversion in the player versus the D to A conversion in your receiver/processor. So, if you use the analog outs, pay attention to the D to A conversion. If you are a believer in differences in analog cables, that also enters into the equation.
On most receivers/processors the 6 or 8 channel analog inputs get no post processing. So, things like room correction and PLIIx cannot be done on the analog inputs. Those receivers/processors that do allow post-processing on analog inputs need to do a A to D conversion before doing that post-processing. So, in that case you do 2 D to A conversions. Fortunately, most of the receiver/processors that convert the analog to digital for post-processing are pretty high quality and do a good job at this. Since I believe your Yamaha does not do room correction or PLIIx, I do not think this an issue. But newer HDMI receiver/processors typically do have both room correction and PLIIx, both of which can be very nice to have.
As I said, there are lots of issues at play here. You really need to do this evaluation based on the properties of a specific receiver/processor and a specific player and whether things like room correction and PLIIx are important to you. Many people report preferences for where the decoding happens and whether HDMI is used or not. But I think that most of these differences come from issues like the ones above, not from a inherent problem with HDMI or analog connections.
