Waterhand could potentially heal Arthur's wounds in battle (plus some other offensive tricks), though there were times in the comics where Aquaman was injured and did not use it to heal (mainly because at the time the water hand was all but ignored). So with the waterhand being utilized to full capability, Aquaman wins easily.
Without, i still think Aquaman's fast and agile enough to keep clear of the claws long enough to take Logan out. But those claws will cut Arthur up, so if he takes too many, he's in trouble.
Yep, Arthur is WAY faster than Logan, and he's strong enough to do some serious damage. If he's got the water hand, the fight will be over before it starts, since he's able to focus his telepathy through it and make it more powerful than ever. Without the water hand......it's a more even match, and Wolverine would take some, but I'd still give it to Arthur.