I use the "Thru" on the DI box.
I haven't noticed any tone "problems", but it does affect the input impedance which is why it is important to have 1M or more on the DI Box. But sometimes I convince myself I hear a difference, even though I seriously doubt I could hear it blind.
So I am actually in the process of building a buffered splitter that sends a buffered signal out and a line-level signal to go straight into my interface. No coloration from the pre, DI Box transformer, or any of that crap and my guitar sees a nice 1M input impedance.
Ha! Reality is, everything colors your signal in some way. More often than not, beyond what a human can detect. Hence why blind tests are so important, human bias is so strong, even though we think we have it under control, we don't. So don't sweat it.
In my case, I need a simple line level battery powered line amp since my RP500 doesn't have enough juice for a power amp. So I figured, might as well add a buffered output and make it 1M. Not much more effort and increases the versatility.