Which of the assassins is best in facing another assassins?

Vayne.

Diana is probably the go to assassin assassin Another pick is Assassin J4. I have used full AD J4 to a lot of success vs Leblanc, Talon, Fizz, Yasuo, etc. Your Lv2 is insanely strong vs them if you land some Q pokes on them (try to hit the minions at the same time to shove to hit 2 first). 2 Q's hit at level 1 and when I pop 2 I immediately E>Q>AA>Ignite and chase for a kill. works way more than you'd expect. and when you roam with ult vs any immobile champ @_@

In my experience, Talon is good vs melee midlaners (most assassins) because of how his harass works.

Watch today's IWCA All Stars games. They are assassin only games.

I personally feel that in a 1v1 scenario fizz,zed,talon and diana are all quite strong. All of them have burst and combo's that are hard to interrupt.

Ekko is amazing because of his ult can really help you. Also mobility shield and some cc.

If you are good with him, zed is a decent choice. You have decent harrass and kill potential

Zed, you can oneshot them before they oneshot you because of invulnerability during your ulti and then teleporting away once you've done your damage and let your ult finish them.

There's only two actually intended-to-be assassins assassins though. Rengar and Kha'Zix. There are no other assassins in the game except unintended assassins like Vayne.