If your DI has a hi-z instrument input, then it's basically an instrument preamp.
Guitar amps or preamps are customised for guitars - obviously. For historical reasons of bad luck, ignorance & greed, guitar players have been stuck with noisy unbalanced humming gear for over half a century. Despite the fact that Les Paul, who invented the electric guitar, invented and used/is using a hum-free balanced pickup. This was because Gibson did a dirty deal, and refused to pay for the invention, but went ahead and made a guitar with Les Pauls name on it. (You can hear the story from the mans lips on the DVD).
So guitars are stuck with noisy hi-z unbalanced crap - while singers get the professional low-z balanced system. This is why a Fender Strat hums like a dog, but the far cheaper SM58 can be used with long mic cables and does not hum. Who gets the best deal?
So that's the basic difference between a mic preamp and a guitar preamp. But the other reason is tone shaping. An SM58 sounds ok into a flat amp with no eq. A guitar pickup sounds extremely bad, and needs a lot of tone shaping - to remove the highs and lows. Also, guitarists have grown to love distortion of all types, which is a greater priority for guitar preamps than mic preamps.
So if you like the sound you are getting, you are good to go. There is no wrong or right (although matching levels and impedances can help if you are getting bad sound). But very often, those classic guitar tones have been achieved with strange and "wrong" combinations of gear.
With guitar, hifi is a dirty word. It's a feature of the history of the electric guitar - almost everything we love about these things is the result of somebody doing the wrong thing.
EDIT - to answer your question - the Mesa is almost certainly unbalanced consumer line level (-10) like hifi gear. You could add an Ebtech Line Level Shifter which also gives transformer isolation, if ground loop hum is ruining your day. Jensen make a better transformer, but like I said - hifi is a dirty word when it comes to guitar.