With regular pens, you have to press the plunger manually to dispense the product. Auto-injectors are spring-loaded, so you press and hold the button and the pen smoothly dispenses the product. I think they are both accurate.
The problem that you describe is, imo, a separate problem. You are trying to dispense an amount that is barely greater than the margin for error. If you are injecting 3 units, and you lose .5-1 unit to inaccuracy in measurement or something else, and then you lose a little more due to dripping or failure to inject completely, you could lose a substantial amount of the product.
If I inject 200mcg in 3 units and lose 1 unit, I am losing 66.6 mcg of the stuff. If I am injecting 200 mcg in 10 units and lose 1 unit, I am only losing 20 mcg. It might make sense to dilute you peptide to make it easier to get accurate and consistent measures.