I think that really depends on your preference and main functions that you prioritize.
I can't really judge how S5 will be as I haven't personally used it, but as for Galaxy Note 3 that I'm currently using....
1.) Bad Wifi Reception (2-3 lower bar compared to other devices hooked up to the same router... this may differ between the device.. mine may be bit faulty)
2.) Speaker... meh... simply horrible
3.) Camera.. not bad, but I'm fairly sure that you could do better
4.) Battery.. I'm content w/ Galaxy Note 3 battery
5.) S Pen. if you use it often, it comes incredibly handy.
6.) Screen. I really can't complain about bigger screen. It offers quite bright and crisp display which is awesome for playing games

I doubt that any better screen will make visible difference.
To simply put, if you want bigger screen and save some money, go with Note 3. Otherwise, I think S5 is mighty better.. or simply wait for Note 4