DIR & ABA are a buffet style of serving your child so i understand why they would recommend it. one of my children has aspergers he didnt want ABA and really showed us he hated it. he became more frustrated and oppositional. he had very high skills in one area but low in others. for the lower skills we used TEACCH method (child lead approach)
i would use DIR its child lead approach especially for a O.D. child.

It's interesting because the two services are basically opposites of each other. The floor time is very much on the child's level and getting into his or her workd while ABA us very adult-led and directed and the child is required to meet the therapist in varying levels. Both can be effective for different reasons. If your child is oppositional behavior due to feeling misunderstood, left out, etc. the floor therapy may help him or her to feel more included and may help you both connect in a new way. If the behavior is more a result of feeling confused, disoriented, or unorganized then ABA therapy can be just the thing to put structure; routine; and clearly defined expectations in his or her life and may give you both the sense of control you've been looking for. It is possible that an ASD child can be experiencing both of these issues as each child with autism is different and each degree if autism can be so different. Your best bet is to try them both and see what works best over a set period of time. You may be able to find a center that specializes in autism that would offer both, some even offer OT/ sensory and speech in the same building depending in where you live, but chances are if you are like many of us you may find yourself traveling to multiple therapy sites different days of the week. That's okay. It's all about finding what works best for your child and family's needs.

totally different. usually experts in one are not well-versed in the other. depending on where you live, one might be state-sponsored and the other not.

I believe it would depend on your child's learning style. Someone who benefits from a reward system in academics should use ABA, one who benefits from the same system to learn life skills should use ABA there. I see no need to rely on one therapy, it seems to dampen the child and make them regress. I would use floortime in the area they are 'easy' learners, and ABA for the challenges. -- homeschooled through preschool and now kindergarten. I always followed their leads and without any therapies they have grown alot, and it has leaned alot towards floortime. ABA for the hard stuff.