In at least some varieties of strawberries, the top of the berry has the least flavor and sweetness, and the bottom has the most, so I don't feel like I'm losing much.
Most mass-produced strawberries people eat today are basically white on the inside and relatively flavorless to the real thing anyway, I don't think most people miss out if they eat or not the top of the berry.
I just rip the leaves off, which is very easy with the variety we eat here. I never would have thought to cut them off. Are your two strawberries different?