The two plots seem very similar:
A sheriff's deputy fights an alternate universe version of himself who grows stronger with each alternate self he kills.
Obviously it's taking form the age old trope of 'What ever you kill makes you stronger' (the oldest example I can think of is tales of eating dragon hearts to strengthen you).
But have the writers/producers/people involved ever said that Highlander was a direct inspiration? If not are there any other clues from either film that tie them together?