Probably lots of preception checks. Not knowing anything about the crime lord and taking a stab in the dark (haha) he will likely be able to outrun the fighter but not the barbarian in a straight up chase. But darkness and knowing the lay of the land as it were might give the edge to the crime lord. You said the PCs have a few tricks but hopefully he has a few tricks of his own.
Without knowing more about the crime lord it's hard to give specific advise.
Depends on what you want to do with the chase and if you want him to get away.
Things like this CAN (if you want them to be) a chance to let some of the lesser taken skills shine. Beautiful one for this would be Knowledge (Local). Where are the ratways and side alleys around here? What of the paths are dead end alleys vs what is not. If mounts come into play, where are appropriate streets to take them down? Where can you find cover if a pursuer takes to the air etc. If it's a flat out foot chase, maybe not a factor, but if they try to cut the guys off, those back alleys may be important. Similarly with working out where the guy might be headed and just dimension door ahead of him to a choke point. Potentially for a monk or ninja who wants to go rooftop running, knowing where the flat and reliable roofs are that you can readily jump between, also important. Knowing where the watch patrols are at this time of night (and if you should avoid them, or if they'll be of assistance)
Next up would be take into account that your going to be (by the sounds of it) running around at full tilt in darkness. Go jogging one night on uneven, ankle depth hole ridden ground with grass on it and tell me how safe you feel about it. I tried that once just as dusk was fading. Pro tip. DON'T. Review the rules on Blindness and decide how much of them you want to apply to running around in the dark. There is one in there about making acrobatics checks every round to not fall over. I'd suggest potentially your looking at perception to notice dangers and anything more than a double move and your asking for acrobatic checks. Blind Fight (which the BBEG should have as night is his normal time of operations) removes this requirement.
Finally, remember stealth. Once you ditch line of site, he can (and might) choose to just drop down a sewer grate and make his way to the harbour via that, or jump into a passing wagon of hay a-la Assassins Creed. A failed perception check might mean he's gotten too far away, or it might just mean he's elected to go dark.