This show at the Bop Shop is being billed as a “tenor battle” between Lin Halliday and E. Parker McDougal, but it’s hard to imagine what these tried-and-true veterans have to dispute. It’s true that they’re both romantics, and full-voiced swingers; nevertheless, they’re too different to be fighting over the same turf. Halliday is an edgy saxophonist whose broken phrases are full of quirky flashes of irony and ingenious wit, and his great strength is his lyricism. What he plays is post-Parker, post-Rollins bop, whereas McDougal is a kind of latter-day Kansas City tenorman: his flowing lines are longer, his sound is ripe and seductive, and on fast numbers his rhythmic playing is ecstatic. He’s a melody man whose solos are cast in classic forms. Both McDougal and Halliday are thoroughly devoted to creating music–they’re beyond style, beyond, as Duke Ellington would say, category, and among the best Chicago jazz has to offer. This “battle’ might just turn into a mutual-cooperation treaty. Saturday, Bop Shop, 1807 W. Division; 235-3232.