Methadone is a very effective pain reliever and it even reported continues to work effectively as a pain reliever once you get used to the high, which removes the need to keep raising the dose. It also seems to keep people satisfied from wanting to seek stronger opioids much better than suboxone. However it does have some downsides, namely, decreases testosterone over time much more than other opioids. And of course it's a very powerful full agonist opioid so you're not going to be clean from opioids, you just will be on a government/doctor sanctioned one that won't destroy your finances or expose you to the risk of black market dealings.
You will experience horrific withdrawals for a long time if you want to stop, but a slow taper will eliminate most of that. of course, you'll have trouble when you jump off even if you taper very low first. But the same is true of suboxone, you'll experience very long lasting, bad withdrawals.
Since you're treating for pain I would think methadone would be a better option. But suboxone does work for some people. It just usually isn't reported to be a great painkiller, since it is a partial agonist vs the full agonism of hydromorphone and methadone (and other strong opiates).
Also induction onto suboxone is more difficult as you have to be in full withdrawal or else you'll experience precipitated withdrawal, and also there will be a period of time when suboxone doesn't make you feel very good, until you get past the acute addiction period from the hydromorphone. Methadone will not have this problem and will fully prevent you from feeling bad from the beginning.