This is just me, but I found the stock "Ninja-like" back tire size a tad unsavory. It would inevitably square-off and leave you with a feeling that you were dropping off the squared off crown when navigating at low speeds like parking lots, around gas pumps or slow corners in traffic. It was like you were on a gyroscope, but when you reduced speed, you sort of fell off the top of the tire and over a corner, and it was very creepy, specially on wet roads. It drove me nuts.
I had read/heard about some having luck switching up the back tire-- going up one size or so and one size NARROWER. It puts you in a class of tire that is very, very common among adventure bikes, and you have more to shop from. The bike/frame swing arm handles the taller tire with ease. My tires don't square off anymore, I have run an Avon Distanzia and am on my 3rd or 4th Shinko 705 on the back. The Distanzia was a good tire, but not really any better or longer lasting than the cheap Shinko 705.
Many will argue that a taller wheel arrangement up front is better off road, and I won't comment one way or the other, let's just say going to a 130 up front maximizes the height of your stock wheel and perhaps there is some advantage. I just don't like skinny tires up front. The 130 fills up the front fork nicely, and you just have to make up some offsets or bracket extensions for the front fender, and I ran new/longer braided brake lines that were the same length, and did away with the crossover line, just me.
Coming from a KLR 650 and other bikes, I must say I like the way the fatty 130 up front handles on gravel or in the occasional sand I may encounter. It's not as dodgy as a KLR. Think "Yamaha TW200"... it's pretty forgiving and I like the set up.
I don't feel that I gave up anything in the "twisties" or in carving up blacktop, or maybe I just can't sense any difference, I like it.
The Shinko 705 I run up front is bi-directional--- you could run it in either direction-- there are arrows specific to your use of it as a front or back tire.
I have run the Distanzia on the back and 3 or 4 Shinkos on the back and am still on the first big fatty Shinko up front. I might replace that one next year, but it has certainly been a cheap date.
Older pic, I was running the Distanzia 150/70-17 in the back but the 130/80-17 Shinko up front.
Again, I was not the first to do this, just my experience but I like it.
Other "experts" will swear you must switch your fork to a DRZ setup, and I say to each his own, I don't need it. Save the money and put it somewhere else!