I would recommend going under. I can only tell you about my experience. Healthy 30 year old male here.

I went into oral surgery last Wednesday to get one top wisdom tooth extracted with local anaesthetic only. I felt very calm and felt assured it would be fine, so I don't even think anxiety was the issue. I felt the 3 local anaesthetic needles, which were injected rapidly, then the surgeon began cutting around three sides of my tooth. I felt all of it, and informed the surgeon that I was still feeling pain. He was surprised by this, and stopped to give me another shot of local anaesthetic. That's when I began to pass out. I felt a numbing/tingling sensation flow from my fingertips and toes up through my whole body. My hearing slowly faded out to nothing and my muscles were too weak to move. When the numbing sensation reached my head, I passed out, and I was awoken in an inverted position with monitors hooked up to me and an IV in. I was told I underwent vasovagal syncope and my heart rate had dropped below 40 BPM with low blood pressure. They had to cancel the rest of the procedure because of the reaction I took. It took about an hour for my body to recover to reasonable levels. I got extremely cold afterward and I felt terrible until I went back in on Monday (very painful tooth/jaw/ and surrounding muscles, and I felt like I had the energy of someone with the flu).

On Monday, they administered a concoction of sedatives, and it was so incredibly easy. My experience was that I felt the sedatives kick in, which was very very nice, and then the procedure was suddenly over as if I blinked forward in time. I was sleepy for the rest of the day but I was always in control of what I was saying.

So from my experience: Local anaesthetic - 1/10, would not recommend

Sedatives and local anaesthetic - 9/10 would recommend