Do people with aspergers have eye contact problems? or are the people with autism the ones with eye-contact problems?

Many people: Difficulty with eye contact has to do with how one processes information and the difficulty is not confined to one type of diagnosis. Many people have such difficulty and inability to overcome it may result in dysfunction . People with anxiety of many sorts may find eye direct contact a bit overwhelming. Definitely worth working on -it can become much easier with effort and self talk.

Both can: Since asperger's syndrome was a disorder on the autistic spectrum (no longer in the diagnostic manual), both disorders can have similar presentations. The difference lies in severity and impairment.

It's a moot point, : since Autistic Spectrum Disorder with levels of severity 1,2 &3 has replaced Autism, Asperger's Syndrome & PDD-NOS as the sole diagnosis. This emphasizes that all people with ASD have some degree of difficulty with social reciprocity including eye contact & facial recognition & social communication plus narrow, restricted areas of interest &/or repetitive, non-functional movements.