Push or pull if the car is in a violent roll you probably are pushing or pulling until it stops crashing. I have not seen remote push systems although they may be out there. The pull systems offer the option of placing the bottles in parts of the car where a push system cannot be reached. I think you are fine with either push or pull.
I used to sell firebottle and I know Don the owner. He pioneered the in car remote fire system. However, the down side of Firebottle is they have a proprietary diaphragm that only firebottle can refill your system with Fe36. That can be troublesome if you don't carry spares. I found out the hard way in 2011. I pulled both handles in a small incident. I had never been in a vehicle fire before... Heck, saw the flash and pulled handles. Next... hopefully not, I will wait a few seconds to see if there is a fire of just a flash! An expensive lesson but one I will remember. Then waited two days while two bottles we overnighted to Wendover. The shipping was as much as the spare bottles. I know Joe Timney sells a good system too and he might be around some of the events or at least if others have his system then there may be a spare bottle in a trailer if you need one.
Buy what you are comfortable with and hope you race your whole career and not us it!
BR