@Connor Personally I can't compare their bites as I have not been bitten by assassin bugs; however, the whole bite and pain aspect has too many variables anyway. Bites are often compared to various bees/wasps stings and cat bites (for tarantulas) as most people have experienced those sources of pain; however, in reality there is little to compare it to beyond that.
Pain is also
very subjective to the person receiving a bite, where the bite occurred, a persons allergic/body reaction, and how much if any venom was injected (as venom varies between bites of the same specimen even).
Take for instance a yellow-jacket bee sting on a arm. I'd rate the pain a 2, while my sister rates it a 8 (out of the typical 1 to 10 on pain, with 10 being the maximum). For me a 8 would have been the kidney stone I passed, and I actually passed-out for at least 10 minutes afterwards. I've had worse pain though and why I rate that kidney stone an 8 - Others may have never experienced that level of pain, or experienced worse pain, so their rating could be much different than mine. Personally when comparing things I try to rate the experience to make the comparison, and as demonstrated, that can wildly vary between people with the same experience.
I've also received a yellow-jacket sting on my eyelid, and would rate that maybe a 5. So if I would use that as a basis to compare to something else it would be vastly different than the sting on my arm. That is one important aspect of the bite pain of various things, as many people have only one bite/sting experience to compare something to. That single bite/sting is also likely vastly different than the bite/sting that is being compared (where it occurred, level of venom, etc).
My mom is highly allergic to bee stings so she would rate that sting much higher too, as she would trouble breathing (and can go into anaphylactic shock). She has to go the hospital to get treated usually after a bee sting; although, some stings have been mild for her through the years and only resulted in some swelling. So even similar yellow-jacket stings are not the same for her, and is a aspect of her allergic reaction and likely the amount of
venom.
Then there are some such as the YouTube user Brave Wilderness that lets things bite him intentionally,
see leaf-cutter ant biting for 60 seconds.
His other videos show a range of bites and stings from jellyfish, centipedes, scorpions, etc. so obviously his pain tolerance/threshold is much different than most.