Wolverine wins this easily (atleast if the writers were honest),
principally for the reasons Sentry touched upon.
Since Captain America was brought up, let us compare the three:
Training:
C.A.-Trained by US military, but not modern US military, but the
WWII one (no offence to any WWII veterans' grandchildren
here, but the average american soldier in WWII was nowhere
near as well trained as his german, british, japanese, or even
russian counterpart). With later added training with Avengers.
B-Trained himself across Asia in various martial arts forms. Later
training with JL (sort of).
W-Trained by Canadian govt., military, CIA, Weapon X program.
Pesonal tarining across Asia. More training with X-Men.
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Purpose:
C.A.-Trained to fight Germans in WWII.
B-Trained himself to fight criminals.
W-Trained initially for war, later (under Weapon X) to fight
super-villians.
----
Experience:
C.A.-Fighting in WWII. Frozen for decades years. Fighting super-villains
with Avengers. Few decades doing so.
B-Mostly fighting street crime and some super-villains, alone (example
Killer croc), or with JL. Few decades doing so.
W-Mostly fighting super-villains, with plenty of fights against ninjas,
samurais, street thugs, etc... Many, MANY decades doing so.
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Bottom line, of the three Wolverine is by far the best fighter. He has
received more training than either of the two, has lived alot more
than the two (I believe more than the two combined), during which
time he's been in a hell of alot more fights than either (or both) of
them, both against common street thugs, and super-villains of many
levels.
Also, Batman rarely physically attacks super-villains (or anyone
stronger than he is), instead using his skill to dodge blows while
deploying various gadgets to win.
Wolverine however, because of his adamantium, healing factor, and
more aggressive nature, pounces on anyone in his way, regardless of
strength (such as the Hulk). This gives Wolverine a further edge, both
in experience, and in psychology.