The HD500 is a dual-path processor that can accept 2 independent inputs. However, the Inputs are not specifically associated with the paths; by that I mean that Input 1 is not dedicated to Path A and Input 2 to Path B. Both Inputs can (and usually are) routed to both Paths. The Input routing depends entirely on the path structure and amp/FX placements in the given preset.

As an example, Input 1 and Input 2 are both routed through a single-path preset. That means if both Input 1 and Input 2 are set to the same physical device (e.g. Input 1 = Guitar; Input 2 = Same) there's a stronger input signal going through the preset, even though there is no second device physically connected to 'Input 2'. Changing Input 2 to an unused physical input (e.g. Aux or Mic) will decrease the level of the input signal that it routed through the processing path.

This is explained much more clearly (I think) in the HD500 Advanced Guide. Here's the clip from it (page 2.6 - 2.7):

About Source Input Signal Routing:

It is important to note how POD HD500 actually routes Source Inputs 1 and 2 through Amp & FX Blocks that are positioned “Pre” position. The following behaviors apply:

• In a configuration with no Amp or FX Blocks in Pre, Input 1 is fed only to Path A and Input 2 only to Path B. Therefore, this is the best configuration if you want to retain discrete Input Sources into Paths A & B.

• Placing an Amp Block or an active mono FX Model in Pre results in a “mix-down” of Input Sources 1 & 2, feeding the same, combined signal into each Path A & B.

• Placing a Stereo FX Model in Pre results in the left channel FX output being fed to Path A and its right output to Path B.*

• The Mixer Block’s Volume and Pan options provide independent control for Path A & B outputs before they are fed through any Blocks positioned “Post” the Mixer.

• By setting Input 2 to “Same,” this effectively routes your Input Source to both stereo Paths A & B (which is how you can feed one guitar input into two Amp Models and/or parallel FX, for example).

*Please also see “Model Types and Mono/Stereo Signal Routing” on page 3•6 for more about how mono and stereo FX affect your signal chain.

Hi

If you set the Input Source settings to Input 1: GUITAR and Input 2: SAME both input sources are routed through your preset's FX and Amp modules thereby effectively doubling the strength of the signal passing along the signal chain.  If you then either want to put something different through the second channel or if you are maybe experiencing input level clipping due to hot pickups, you would change Input 2: to Aux, Variax or whatever to cut the signal level going through the preset by having your guitar signal only coming through Input 1.   So, what you are hearing when you say your guitar signal sounds thinner when you only have one input source set to Guitar is actually the result of only having half the signal you previously had with both input sources set to Guitar passing through the preset.

However if you mean that you already have Input 1 set to Variax and Input 2 set to Aux and when you change Input 2 to something other than SAME or Variax your sound quality changes, then it shouldn't make any difference. 

Nick