Why the noise

Ok, noise can be coming from a huge variety of sources. Could be the guitar itself. Is the wiring properly shielded? Is it a single coil Strat type or a humbucker Paul type. Single coils are more prone to noise. Cheap cables can also be the culprit. If you're not using a power conditioner you should be.
Amplitube itself can be very noisy. Do you have the same problems recording directly into your DAW? Tho theoretically you should be able to plug directly into the line input....line level sources like keyboards and guitars are NOT the same and often going direct like that with a guitar will create an impedance mis-match giving you the results you experienced.

would a DI Box be a solution?

Sooo.....you noticed improvement with the ART unit. But it's really not the right tool for the job.
As you have already suspected, you will get better results with a dedicated DI box. A DI is always
a good idea and an absolute necessity when using active pups like EMG's.

Radial makes THE best DI boxes IMHO.

That being said we can help you better now and in the future with a bit more info......if you will post your system specs in your signature, (see my sig), we will be better able to troubleshoot your problems. Without knowing what type of pc you're running, what OS you're using, what DAW etc....we often can't recommend a "simple fix"

If you have not already done so please READ THE MANUAL!