Moto G is waterproof or at least water resistant, 620 is not.
Moto G can be customised, you can have Xposed Framework on it as it's bootlaoder can be unlocked right from motorola website, 620 is stuck with same software forever.
Moto G is android, more apps, better apps. 620 is windows, almost no apps, well maybe more than blackberry.
Perhaps one thing has 620 has that moto g does not is manual ISO and exposure settings for camera. That is mainly due to android restriction, at least til jellybean. Having said that, moto g does have usb otg, can you can run literally any camera with it, even dslr, you can run an external 1TB HD with it, playstation controller, mouse, keyboard, you can literally use your moto g as a mini pc. Moto g does not have mhl but you might be able to output with chromecast or miracast.
Moto G also has the following:
faster CPU, more battery life, higher pixel density (329 ppi) means better graphics, more ram, bigger screen, better front camera for skype etc (1.3 mp), has gorilla glass 3 which is scratch resistant, has 16 gb internal storage and coupled with usb otg sky is the limit, has a radio, has 2 microphones one noise cancelling resulting in better call quality, has a gyroscope, lower SAR level (less chance of getting cancer), if youre rooted or have jellybean has call recorder, has appops for privacy management meaning you dont have to w orry about angrybirds taking your photos.
Moto g comes in two flavours, one that was released at beginning of 2014, and that is 3G, and another one available nowadays which is 4G. The new one is I believe made by Lenovo, the original one was made by Motorola Mobility. If you can, go for the original one, that came in jellybean, and that means lots more stability, more options like call recording apps would work, and NEVER update it to kitkat. I have mine rooted with Xposed Framework, stock rom. If you go on xposed, you will never look back.