I'm interested to know what kind of pickups you guys have. Because it was well known that passive pickups lost a bit through the redeye. That's why they have two inputs in the new one, an active input for passive pickup and a passive input for active pickups. If you're using the right input with your pickup type in the new model I'd really like to hear exactly what the DI is changing in the sound.
If you read the instructions on the redeye it also states that the gain coming from the through output could be slightly higher or lower depending on the loading sensitivity of your amp. There is a +3db level switch INSIDE the DI to account for this, if you are using the active input. It also states that if you're plugging into the passive input, you'll lose 3 dB of signal because of how it's routed internally.
So to the OP, it shouldn't be sacrificing any tone, but depending on your pickups and the input you're using, you may just need a tiny bit extra gain on the amp when running through the redeye. Check that manual!