The Collaborative International Dictionary of English v.0.48:

Rival \Ri"val\, v. t. [imp. & p. p. Rivaledor Rivalled; p.
   pr. & vb. n. Rivaling or Rivalling.]
   1. To stand in competition with; to strive to gain some
      object in opposition to; as, to rival one in love.
      [1913 Webster]

   2. To strive to equal or exel; to emulate.
      [1913 Webster]

            To rival thunder in its rapid course. --Dryden.
      [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

41 Moby Thesaurus words for "rivaling":
   a cut above, above, ahead, ascendant, better, capping, chosen,
   competing, competitive, cutthroat, distinguished, eclipsing,
   eminent, emulous, exceeding, excellent, excelling, finer, greater,
   higher, in ascendancy, in competition, in rivalry,
   in the ascendant, major, marked, of choice, one up on, outstanding,
   over, rare, rival, super, superior, surpassing, topping,
   transcendent, transcendental, transcending, upper, vying