So the probability to roll any given number on a d6 would be .16 repeating, so we can round up to .17. The probability of rolling any number on a d8 would be .125, which for simplicity we'll round up to .13. In order to get a number equal to or higher than a 6 on a d8 it would be about a .38 chance. Basically 6 in 10 rolls on a d8 will be within the value of a d6, but 4 in 10 rolls will be higher.

Now the part we don't need any math for: there is a .0 chance of a d6 rolling higher than a 6. If you want the highest numbers possible then choosing a smaller die will fail you. Not only are the individual odds of rolling a number available on a d6 smaller on a d8 but the d8 has a higher maximum than the d6. There is no real benefit to rolling two die of different values other than for novelty or to abide by a rule, unless you want smaller numbers intentionally.