Tough one, to be honest.
Slender:
+ more cardslots
Multiple:
+ more iconic LV design
Taïga:
+ the only true Men's only leather at Vuitton, very discreet and masculine
- since its grain pattern is made of both horizontal and vertical lines, it can be a little softer and less durable as Épi. Taïga leather bends more easily, and in back pockets will lose its shape more quickly
- the Iconic colours are gone now, Taïga was a similarly duo-toned leather as Épi, it had a darker shade on the bumps of the grain, but not anymore. the iconic Ardoise (which was a dark charcoal) is replaced by a simple totally black version now. Kinda sad.
Épi
+ the most iconic Vuitton leather pattern of all time, also very discreet
+ more durable, since the lined grain is more resistant horizontally
+ although most Men's Épi pieces lost the dou-tone effect as well, the pattern in itself can still provide that Vuitton-ness. And Noir Épi is an absolute classic no matter the grain tone
- but if bent too much, either by opening it waaaay too much, or at the corners by a back pocket, Épi will wrinkle in a less pleasing manner as Taïga
To sum it up, I'd choose an Épi Slender. And would have it stamped. If he is into Vuitton or the whole boutique experience that comes with a stamping, then I wouldn't stamp, but would go back with him after the birthday, so he can have that extra too. But if he is not at all into that, then I would just order it that way. Monogramming is a nice touch, can't imagine a man who would be against it. It makes it truly his. And silver foil, all the way.