Disclaimer: I am not an expert. I am learning as I go. The things I think I know may be incorrect.

That said, here is my 2 cents. The Vox amp (and really any standard guitar amp) you are using will color the sound of the POD if you plug it straight into the guitar input. If you dial in a super setup listening through headphones and then plug it in to the guitar input it will not sound the same. The tone circuit and the modeling of the amp itself change the careful preparations you made (or the tone of the preset). Also keep in mind that the POD emulates speakers which in the real world can sound quite different from one another. So as I see it, feeding a speaker/mic emulation into a speaker with its own character changes the sound.

There are several things you might do to mitigate these issues. Using the effects loop on an amp may cut the tone section of the amplifier out of the signal path depending on how its implemented on the amp. If you have to plug directly into the guitar input on the amp try setting the tone controls on the amp to "flat" and work on the model or preset on the POD until it sounds better. Sometimes changing the speaker used or the mic used in the POD settings can  help the tone when you use it with a guitar amp. You may also find that using the POD directly into a PA type amplifier and speaker setup may sound better. I have also found a few keyboard amps with tweeters built in tend to color the sound less if you use them with a POD.