Analog vs. Digital Connections
If your A/V receiver or preamp/processor passes an analog signal coming into its multichannel audio inputs directly to its analog outputs with little more than gain adjustments, the player must perform channel delays, bass management, and so on. This will work, but few players offer the setup flexibility of a mid- to high-end AVR. It also means that audio features such as digital equalization, which is likely to be available only in the AVR, is unavailable. Competently designed and calibrated equalization may well make more difference to the final sound than the relatively subtle benefits of higher-end DACs in the player.
Some AVRs and pre/pros can process signals coming into their multichannel analog inputs, but in doing so, they first convert the analog input to digital, because channel delays, bass management, equalization, and so on are nearly always performed in the digital domain. In that case, the analog audio from the upscale analog outputs will pass through the ADCs, DACs, and analog output electronics in your AVR, and the likely result will be no net benefit from the player's supposedly superior DACs. You might even hear inferior results because of the extra elements in the signal chain.
What does your AVR do with those analog inputs? You might be able to find out from the manufacturer, but you should still do the comparisons suggested by Scott to see if you have a preference. You may well hear no benefit from the forest of analog cables you'll have to deal with to make use of the player's analog outputs.
Also, don't forget that those analog connections are subject to all the usual analog issues, including the importance of cable length and the strong opinion held by many audiophiles that different analog cables sound different. The latter is a subject for a very long book; I bring it here up only to put it on the table.
And while some players such as the Oppos can output a DSD bitstream directly (DSD is the encoding scheme used on SACDs), not all AVRs and pre/pros can accept it. That's why a player must offer the option to convert DSD to PCM in order to pass it on to the receiver via HDMI. If you play an SACD from the analog outputs, the player must decode the DSD to analog, which, in most cases, means it must convert DSD to PCM in order to be compatible with the player's onboard, PCM-only DACs. (The Oppo seems to be able to decode DSD directly to analog, but this is not true of some other universal players.)
My comments so far apply primarily to high-rez audio from Blu-ray, SACD, and DVD-Audio. But what about music from 2-channel, 16-bit/44.1kHz CDs? After all, CDs are still widely used to deliver the music that enthusiasts are likely to play on any universal disc player. After you determine whether you prefer HDMI or analog connections for high-rez audio, you should also try the coaxial and optical digital connection to your AVR.
For another discussion of this issue, check out Kalman Rubinson's article over at Stereophile.com.