I am using a 2N2222 transistor circuit to drive 2 Relays which are parallel to each other. Can I use MMBT2222 (SMD) transistor instead of 2N2222 (Non SMD) transistor? What will be the disadvantages?
Assuming (and you shouldn't, and should read the datasheets carefully) the same die is in each package the differences will be mostly thermal (there might be some small differences in parasitic inductance and capacitance, but that's not very important with a sluggish old transistor like the xx2222 (ft = 250MHz).
Thermally the SMT transistor behavior changes a lot more with the PCB design (the amount of copper connected to the lead frame and so on) so when you are doing your calculations you need to pay attention to the exact test conditions under which the power dissipation is specified. If it's got a square inch of 1 oz (sorry for the non-metric units) copper connected to the collector tab and you have a thin single layer board with 0.5oz copper you will get more temperature rise.
The "real" 2N2222 is packaged in a hermetic TO-18 metal can and has the best thermal capability. However there are no JEDEC police, as far as I know and most parts that are called 2N2222 are more like PN2222 (TO-92 packaged), with less thermal performance and not hermetic. The MMBTxxx are SOT-23 and generally capable of even less power dissipation. It's possible someone makes SC-70 transistors called 2N2222 as well, and they would likely be even smaller and less capable of dissipating power.