I think the only difference is the tire width, not height. If that be the case the speedo won't change. As to the width, measure all clearances to frame members to make sure no tire rubbing will take place .
I don't know so much about motorcycle tires, but with car tires the 2nd number is the aspect ratio of height to width. If the if the height ratio stays the same, 70 in this case, the width of 150 to 160 will also increase the outside diameter. Might not be much.
Meaning of 160 / 70 is 160 mm in width and 70% of this in hight, in this case 112 mm.
On a 150 / 70 it is only 105 mm in hight that means your OD will increase by 14 mm, makes a little in speed not much.
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