Our ds has Asperger's/giftedness and lasted about 2 years functioning in public school. He really functioned well in the classroom and got along great with teachers, who were super-positive toward him. But he couldn't handle the expectations the older he got, because things get more complex.
As long as reading was technical, he shined. When it became a way of acquiring complex information, often independently, he was constantly lost. When his super-science and math interests looked advanced he seemed to be the smartest kid in the class, but when it came time to complete classroom papers or homework with a little bit of independence he fell apart, an he did have a teacher attempt to embarrass/shame him about this. (It was isolated but clueless on her part since not only did she offend me, he is completely unable to be embarrassed by her.) The more focus that was needed, the more the high stimulation of being surrounded by others and the need to finish things on time and follow through started to limit his functioning.
He has social functioning areas that look more like a 4-6YO and he's 11yo now. When he was 7yo-8yo his immaturity blended in with the classroom but within a couple of years he was really out of step because he had stayed in that place and the other kids were moving along.
He was bullied and in ways that the teachers didn't really understand. He was inappropriate to other kids in ways they weren't being proactive enough with. Because he doesn't self-monitor or understand what everyone else understands.
I know that although officially these dx are distinct there is so much overlap that the distinctions are fuzzy. For us the difference between an autism dx and an asperger's dx was that ds was definitely not delayed verbally. (Though he does have many ongoing practical "pragmatic" language delays, he used language quite early and that's what they counted... But if I take his other advanced areas into account his language was later in comparison.) If he had been delayed verbally, it would have been autism. His skills are extremely uneven... He has definite social problems but I will say that the teacher's observations included in his diagnosis material claimed he did not. A lot of people have said he was fine. He is affectionate, friendly, etc. However, even now, he engages in "parallel play" like toddlers do and he also engages in "parallel conversations" in which what he says has very little to do with what the other person says. He has trouble with being aware of others. A few slight variations on the answers given in the evaluation can make an occasional incident look like a pattern or vice versa and these can make a difference. There were a few conflicts between different observers in our reports, too.
I think you should proceed with this diagnosis. It is an important tool for you, and you should use it in any way that brings benefit. You should not expect to be forced to accept one IEP option because that is what they always do with autism. But those things that benefit classic autism benefit Asperger's too--the supports are pretty much the same. Use them.
The dx can definitely change with age, anyway, and you can support his issues with any of those dx. Half the time, I think of my ds as autistic FWIW, because information related to autism tends to also apply to him. Whatever the dx, I think that age will help you to confirm it as well: Symptoms become much more obvious with older kids because-- for instance-- social behaviors that are close to normal at 4yo are very atypical at 8yo and 12yo. Significant gaps will tend to get larger with time and help clarify your ds's needs.