If you're looking to play for the tactical/strategy aspect of the series, I would say Awakening is the better way to go. It gets you into battles at a faster clip, and its combat system is more intricate as it hinges on the iconic weapon triangle system, something that Three Houses does away with. The challenge is also higher, though not insurmountably so, thanks to being able to adjust difficulty -- and it's better paced.
Three Houses has the better story, but at the cost of the included RPG/school simulation elements, which, to me at least, felt overbearing at times. Battles felt less satisfying, in part because they play out more straightforward without the aforementioned weapon triangle system and simplified mission objectives, and the challenge, even on Normal and Hard, felt disproportionately easy. (Maddening, by comparison, feels a little too unfair.)
An an entry point into the series, you really can't go wrong with either title, but I do feel Awakening is more conducive to being a more genuine Fire Emblem experience.