The main things you give up in Presnensky are safety varies significantly by sub-area — Patriarch's Ponds area is safe, other parts are not, documented concentration of rough sleepers and petty criminals around several metro stations, particularly in the evenings, 2,846 crimes including robberies and muggings recorded in Presnensky in a single year (Russia Beyond / Moscow Prosecutor's Office data).
The strongest reasons to consider it are Moscow City financial district — impressive modern skyline and observation decks, Patriarch's Ponds — one of Moscow's most charming and upscale residential areas, association with Bulgakov's The Master and Margarita for literary tourists.