Honestly I think a lot of it would depend on the mixer and the quality of the Mic pre. If you use a DI with a line level device like any of the many DSP devices it actually takes a strong signal, lowers it, sends it across the length of the cable, then boosts it again at the mixer. If you have a quality mixer with good mic preamps, then you probably won't hear much difference.
If you use a line isolator, it is still transformer isolated just like a DI which will protect your digital device from phantom power and noise but the signal is not attenuated. It hits the mixer at line level. Some mixers have the ability to bypass the mic preamps and accept a line level signal, so you are removing the need to re-amplify the signal and you get a stronger signal to help maintain your tone over longer cable runs.
My regular mixer (a Presonus StudioLive) is currently in the shop getting repaired so I recorded the following clips using my Allen & Heath Zedi10. It has buttons on it for line level if you use the XLR input, or you can use a balanced 1/4" input. My samples were recorded using the two outputs of the HX Stomp. One into a Radial JDI connected to the mixer's XLR input on channel 2. The other output connected to a Walrus Audio Canvas line isolator running across the same length, same brand, XLR cable into the "Line In" 1/4" jack using an XLR to TRS adapter on channel 3.
If you listen on good speakers, you can hear what sounds like a little more top end with the LI vs the DI...but the DI does seem to have a little fuller sound. Of course, that could be due to the JDI as they do have a Jensen transformer in them which is known to impart some character.
Here's the clips:
DI
LI