When comparing acid strengths use "CARDIO"
C-Charge (More negative stronger base=weaker acid)
A-Atom (More electronegative weaker base=stronger acid)
R-Resonance (More resonance=more stable base=stronger acid)
I-Induction (More electronegative atoms attached, better they withdraw=more stable base=Stronger acid)
O-orbital (sp>sp2>sp3..electrons closer to the nucleus=more stable=weaker base=stronger acid)
In your case, if we look at the Conjugate bases, -NH2 and -C=CH2.....Start with C...since both are negative then move to A, since N is more electronegative than Carbon, NH2- is the weaker base and therefore NH3 is the stronger acid...
Hope this helps..
EDIT: You may want to know the pKa: For Ammonia the pKa is about 33, an alkene pKa is about 44.
THE CARDIO WILL FAIL YOU WHEN COMPARING LIKE AMMONIA (PKA 33) TO A TERMINAL ALKYNE (PKA 26) BECAUSE AN SP LONE PAIR IS MORE STABLE THAN AN SP3 LONE PAIR.