Depends.
Depends also largely on what you mean with "games like battlefield"
Battlefield has become sort of a casual FPS, where you won't notice the difference too much.
In highly competitive games like csgo or ow, the response time _can_ but doesn't have to make a difference. It's all depending on your visual perception.
I think 3ms is the threshold where you're not physically fast enough to respond anyway
Overall 5ms won't be an issue unless you got jedi-esque reflexes and perception.
Main question is: is it worth it.
Outside of a competitive or even semi-pro context you can do with one death more or less in a situation. Neither screen will make you a better player or give you a severe benefit over your opponents and if you got 27-10 or 26-11 at the end of the round - who cares.
The IPS will look nice usually in terms of picture quality. However again if you can't stand IPS glow or are very sensitive to backlight bleeding the TN will be the better choice.
Even more if you don't care for all the additional beauty because you get so caught up in the battle scene and do indeed get very competitive when gaming.
See what I'm trying to say?
Depending on your preferences, both would be fine.