Does an employer have to give preference to an applicant with a disability over other applicants?

No. An employer is free to select the most qualified applicant available and to make decisions based on reasons unrelated to a disability. For example, suppose two persons apply for a job as a typist and an essential function of the job is to type 75 words per minute accurately. One applicant, an individual with a disability, who is provided with a reasonable accommodation for a typing test, types 50 words per minute; the other applicant who has no disability accurately types 75 words per minute. The employer can hire the applicant with the higher typing speed, if typing speed is needed for successful performance of the job.

For additional information, take a look at the following resources:

FAQ: Does the ADA require that an applicant or employee with a disability be qualified for the position? 

Fact Sheet: Reasonable Accommodations in the Workplace