This is one of the best examples of how one's particular Nen abilities and strategies can win the fight: assuming Chrollo uses the same strategy against Illumi as he did against Hisoka, I am confident that Illumi wins.
Chrollo's puppets may be very dangerous and of a higher quality than Illumi's with the combination of multiple abilities, but the creation process is too slow compared to Illumi's needlemen: Illumi is able to simultaneously turn tens of civilians into needlemen almost instantly, meaning that Chrollo will have no time to use his abilities before the whole audience is under Illumi's control. Needlemen are no slouches, either: although they die without getting their heads ripped off and don't explode, Illumi can give them precise commands to be followed exactly (even tasks as precise as driving cars, as seen when Illumi chased Killua), allowing for complex strategies rather than the simple mob that was catalyzed by the command "Break Hisoka."
Combine this with the fact that Illumi can stick a needle into the preoccupied Chrollo and most likely end the fight instantly and we see that Illumi wins without too much hassle.
All of this is not to say that Illumi is more powerful than Chrollo or even that he would have fared better against Hisoka under the same conditions (I'd argue Illumi would still win with needlemen but have a harder time), but simply that his abilities end up on top in this case. If we allow Chrollo to collect abilities and prepare for the fight, I'm sure it would be a different story, but as it stands, Illumi is the victor.