Not much of a fan of tiers but it's the best way to give estimated guesses on where their strength lies.
Top Tier
Kuma - Everything about this guy just seems hax. He can practically teleport, paw whatever he wants to away which probably includes Logia-type users, he's a pacifista, and he can send people farfar away by touching them. Wouldn't know if he'd actually be the strongest of all, but he's definitely at the top. Only reason he wouldn't rank highest is because he can only do this with his hands, which make attacks from the back a bit harder to manipulate and counter.
Blackbeard - He has a Devil Fruit capable of rendering others ineffective, controls gravity and is, even without Fruit, a strong fighter. He was able to scar Shanks and kill a 4th division officer without any Fruit. His only real weakness would be the fact that his Devil Fruit won't help him a bit when damaged – Ace probably could've killed him had he launched a full-scale attack on Blackbeard whilst he was rolling over the ground in pain, and surprise attacks could be devastating. This would leave him, too, competing for first place.
Mihawk - He's the strongest sword fighter of the world, simple as that. He can probably cut whatever he wants, has immense speed and technique, and horrifying strength. The problem with him would be that he, most likely, doesn't have a Devil Fruit. I'm not one to tie strength to Devil Fruits only but unless you're fighting in water a Devil Fruit brings nothing but an advantage; Kuma can teleport and turn air into a cannonball while Blackbeard can repel and attract everything around him. Also one of the strongest Shichibukai.
Middle Tier
Moria - It seems many people underestimate him because he let his shadows clean up his mess. Thing is, if you have a Devil Fruit which allows you to manipulate shadows in such a way, it'd be a bit weird to call it cheating when you use it. Even without his shadow army and Oz, he would clearly be a strong fighter. If he steals your shadow you're in a coma for two days, a 48 hour period of time where he can kill you. Besides that he has his Doppelman, which allows him to swap places whenever he likes while this Doppelman is a bitch to fight as he can't be hurt -- a mini-logia-you. Besides this, Doppelman can also fuse their shadow in others and control the shape -- I don't know whether this allows for opponent control of some sort, but it could at least be used to strengthen one's own body. His biggest weakness would be his ego. If he hadn't taken all those shadows, the Strawhats probably would've died. Had he not taken an amount that gave him trouble staying conscious but only half of that, the Strawhats probably would've died. Had he simply killed Luffy, Sanji and Zoro after he took their shadow, the Strawhats probably would've died. I'd believe him to be at the top of the middle tier, though this could only be safely said when more of the Jinbei and Doflamingo is known.
Crocodile - As he is the first Shichibukai taken out and also carrying one of the lowest bounties in it, it'd be easy to pick him as the weakest but on the other hand, he has a sand Logia. Though Haki and fluids seem to render his ability to avoid damage when hit useless, he still seems to be able to put up a fight without this, simply by avoiding punches. He could've killed Luffy three times had he simply cut his head off when he had the chance, but seeing that that would've ended this story a bit too soon Oda couldn't possibly let him. Besides the fact that he can create blades out of nothing, he can also suck the fluid out of people the moment his hand touches them -- something which could kill pretty much anyone -- and, as a person, he's quite cunning both in and outside of battle. As the case with many OP enemies, his ego, pride and shounen logic caused his downfall, but even with that working against him he would score fairly high.
Doflamingo - We haven't seen much of his power, all we know is that he can do something puppetry related, but with that we can assume some of his powers. It seems obvious his puppetry powers work only on the somewhat weaker characters -- stronger ones still have to put up a struggle but if he could control the strongest characters he would've been a bit too much of a hack for this world. With that, it would be safe to assume he can at the very least control single limbs of stronger opponents, probably move lifeless objects about and more attacks in the lines of. He seems a bit like someone who excels at slaughtering the nameless masses, rather than taking on the stronger named fighters, and it would appear he got such a high bounty mainly for being the leader of many shady organizations and businesses.
Jinbei - Nothing is actually shown regarding his fighting power, but we can at least speculate; as a fishman he would automatically have the advantage of starting out at ten times a human's strength, which would probably only go up as he trained, and it would seem logical if he has some skill in fishman karate. Besides that we can safely assume he doesn't have a Devil Fruit and that he probably fights using Haki. He seems a bit like a somewhat slow fighter with immensely strong attacks. With this, he would not have much advantages to any kind of Devil Fruit while it would give him some he'd be weaker against -- which is the main reason why I placed him in Mid Tier. I would go and say he's somewhere in the lower part of this Tier, but I'm guessing this would come from the fact that I don't really like him -- I mean, he's a fish D: -- so I can't really give a proper guess on his placement in this Tier.
Lower Tier
Hancock - Not saying she is weak -- if Sengoku didn't acknowledge her strength she wouldn't be made Shichibukai, obviously -- just saying I think she's a bit weaker than the other Shichibukai. Judging by the powers she's shown so far, the petrification attack seems to be one of the stronger moves she has, as it's the only thing she tried to attack Luffy with, not trying anything else besides that kiss-attack. So yeah, that combined with her Haki-potential seems to make her someone who can take down numerous enemies at once, probably more so than any other Shichibukai, but would be a bit weaker to the stronger names.
Just giving a speculation of what I think seems to be the case. I personally don't like some of these character's placement; I'd rather see Hancock as one of the stronger ones while Mihawk as someone far lower but ehh, this seems more plausible to me.
