Existential doubts

How about you abandon hope?

Given how both banners have literally 3 options each, your chances of getting Mordred are the same as your chances of getting Nightingale.

Following that logic, and assuming you ONLY want Mordred from the Saber banner and only DOESN'T want Nightingale from the Berz banner, your best shot would be the berserker banner since you have a 66.66% of NOT getting Nightingale, while at the same time you have a mere 33% chance of pulling Mordred out of all Sabers.

Both banners will come with risks for you. You can't avoid it unless you magically decide you need another Nightingale or if you consider other Sabers as well. You have slightly better chances of NOT leaving unsatisfied if you try the berz banner. Think hard about who would make you happier and if you're willing to take this risk for them. But remember that the higher the risk, the higher the reward should you be successful. Just don't rush a decision you might regret, and remember that it's not the end of the world if things don't go your way. You can always try again the next time.

Stop expecting to get what you want out of gacha. You'll find your life is a lot less depressing.