Interesting thoughts. (Also you taught me a new word. I knew sentient, but not sentinent.)
I think that, usually, they don't. However, I could imagine, just as it is rare for a sword to be sentient, it might also be rare for a sentient sword to be sentinent.
It'd be interesting to have, say, a holy avenger that has the mind/soul of a former paladin able to feel each blow (and perhaps motivate it to try to convince its owner to use it less). Or perhaps a bloodthirsty sword?
I first read sentinent as sentiment. I like to have intelligent items have a story behind them. For instance, a bowstring woven out of a loved one's hair, and imbued with a bit of their personality. Perhaps a power or two tied to the relationship between the wielder and the person whose hair it is.
I could imagine feelings of love when the bow blessed the wielder, felt by both of "them".