Starting a new piece
I usually read without the bass the entire piece, getting what feels like the piece's natural tempo and feel. Then I play it at that concert tempo, noting where I falter. Then I practice the faltered areas slowly and with great concentration, always with the concert tempo and feel in my mind, driving the practice towards that goal. I also make it a concerted point to not use articulations in slow practicing that I do not intend to use up to tempo!
So, both ideas that you mentioned are used, always with the
Goal in mind!
Best to you,