In my case, both.
I need strength for my job since at any given time I might find myself in a physical altercation with a violent felon (and have hundreds of times).
I want size because most of my life I've been on the thin side and only since I've been lifting the last 3 1/2 years have I been in the 'looks good' side of things.
Fortunately both can be trained for simultaneously. How successful have I been? Well, I've not arrived yet where I'd like to be, but that is the fun of it i.e putting in the sweat equity. But over the last 3 1/2 years I've gained 30+ pounds, lift heavier than when I was half my age and get compliments on my looks.
So far so good

Body building isn't everything...it's just that being small, weak and puny really sucks.
Current: Age 44 ht 6' wgt 186
(lbs)
Squat 230 Bench 225 T-bar row 165 Press 135
Goals:
Squat 240 Bench 230 T-bar row 170 Press 150
My Log