According to the premium edition of the Dungeon Master's Guide (2012) when a creature activates the bead of karma that's found on the standard or greater strand of prayer beads, for 10 min. the "[w]earer casts his spells at +4 caster level" (267).
Thus the increased caster level affects any spell the user casts, no matter what class the spell's from, and no matter if the spell's arcane or divine.
No more's said about the bead except that "the bead… of karma can be activated by any character capable of casting divine spells" (ibid.). This is disturbingly vague: ask the DM if this means that, for example, a rogue with 1 rank in the skill Use Magic Device and that has two divine scrolls of cure light wounds—one in each hand—is capable of casting divine spells. This DM would say No, but others may disagree. Similarly, it seems legit to this DM to allow a strand's wearer to activate the bead then give the strand to another creature to wear so that the other creature can benefit from the bead's effect for its remaining duration without the other creature having activated the bead's effect… but this DM can imagine other DMs taking issue with that.
Note that the bead of karma doesn't effectively raise the wearer's caster level in general: the bead's effect occurs only when the wearer casts a spell, at which point that spell is cast at +4 caster level. Prior to casting a spell, the wearer's caster level is what it is normally, even if the bead's effect is active.
Also note that the standard strand of prayer beads' price is changed by the premium edition Dungeon Master's Guide from 25,800 gp (the price of a bead of healing plus a bead of smiting hence—without this change—allowing free standard strands of prayer beads on which are only beads of karma) to 45,800 gp.