Recurring expenditure of power bill, due to continuous charging. In case of inverter the AC supply is converted in DC , by changing sinusoidal wave form to half wave, which causes almost 15% loss in power.( in other words, you pay 15% more for the charging that the actual current used for charging ). Second point is, when you convert the AC to DC through rectifire, *( which is basically thyrister control )third harmonics are developed, hence the severe distraction of the wave form, which is not good . Third point, when you use battery power, its DC converted in AC through transformer, there is again loss of power to the tune of 15%.
Last point is , the battery life is just 2-3 years. If you dont replace the battery, the power back up timing reduces considerably.
Up to 2-3 KVA inverter is good, but beyond that , one should go for the generator.