A good direct box is what you are missing.
Yeah, you can get a "decent" sound with sims without a good D.I., but I guarantee you are going to see the night and day difference in the quality of your sound. I don't really see this talked about that often when discussing amp sim sounds. Buy , try, test, don't like it send it back (but you won't).
Something like this one (highly recommend the Countryman 85, worth it's weight in gold and built like a tank). A staple in many major studios, and for good reason.

Slugbaby
Find a sim of an amp you like.  Run it clean, and tweak the amp knobs until you get a decent clean sound.  Then increase the gain slowly (either on the amp or with an OD pedal), and you should get a solid overdriven guitar sound.  Be careful not to overdo the gain, that tends to ruin a sound pretty quickly.

This^^
 
I had the same experience with the version of TH3 that came with Platinum. Their instructions for setting the input level gave horrible results whether on clean or overdriven sounds. When I cut back the input gain, the sounds improved dramatically.

henkejs
When I cut back the input gain, the sounds improved dramatically.

Line 6 PodFarm has the same issue. 
I got a better DI because I thought the signal was was weak and that a clean hotter signal would improve things.
It didn't. The hotter signal made everything sound like crap.
Try lowering your input.

Ive found that no matter what di im using, when using th2 or th3 i always find myself putting a distortion pedal in front of the distorted head and mixing the both gains for a decent distortion. Usually seems like one or the other just sounds bland by themselves. But then again as stated above, if youre not careful you risk having way too much gain and sounding way overdriven. Best thing about sims though, you can change everything again later, haha.

OK guys. Probably something really obvious I'm missing here but:
 
When I turn the channel gain on the Tascam interface right down to virtually zero, on the TH3 interface when I strum my guitar, the input levels are still hitting 50% on the meter. I can't reduce the levels any further via the Tascam yet they're still quite 'warm' on the TH3 meter. What's going on? How can I reduce the signal level into TH3 more than I already have?
 
Dave 

∞

mister happy
It seems noteworthy that you have solved your concern by purchasing a dedicated 1MOhm buffer stage. 
 
Did anyone ever ask if you have flipped the switch on your Tascam 4x4 on "IN 1" or "IN 2" from "MIC/LINE" from the 2.2kOhm LINE input setting to the 1MOhm "INST" input setting?
 
If not, give it a try and see if this replicates what the ZBox provides.
 

 
^^^^This.

If you're using Sonar, first in the signal chain should be the tube sim, I use this to level the signal and add some 2nd level harmonic distortion. If you're after a crunchy over driven sound perhaps try 1 instead of 2 if you're after a really 80s transistor type over driven sound. I tend to use 2 because it's softer on the highs. Just listen when you dial in the distortion. I then tend to use a low shelf filter - normally the one supplied with GR4...just till off a gentle amount because you will roll off more. I tend to then feed the signal straight into an amp sim. For over driven transistor type crunch you can't go past a marshal sim, if it's softer then a hi watt. You could alternatively add an overdrive pedal into the signal chain before the amp sim. What most people don't quite understand is, that to achieve an album type sound from a guitar sim you then need to mix it properly. After the amp sim I will then use an EQ and compressor. I use my ears to decide which I want first. Also, I use Wave's analouge emulation plugs. So for me, there are some great options that really add to the sound. For example, Kramer's Pye stuff is excellent for rock guitar. Eddie Kramer used a lot of these EQs and compressors on Hendrix's music and also Zeppelin. If you're after a pop type guitar sound you can't go past the TG12345 emulator - The Beatles and Pink Floyd. The Schepp Neve EQ is great too and finally any of the SSL stuff is great on guitars particularly on 80s style over driven guitar. Most of these plugs can be picked up for 30 bucks a pop now too...sweet.

Ben

I'd see if I could get a refund, if you're not satisfied with the guitar tones. I think Overloud makes some amazing EQs, but I think there are better options for guitar tones.