I'd prefer to both look strong and be strong. If forced with literally only being strong or looking strong, but not actually being strong I would prefer to just be strong.
That said it's pretty easy to be big AND strong if you eat enough AND have average or better genetics. Waaaay too many guys are so concerned with their 6 packs and "looks" that they will never graduate to actually being strong in the first place compared to a strong lifter(ie. weightlifter, powerlifter, strong man etc).
Everyone has varying opinions on what constitutes strong. I do believe that most could come to a reasonable agreement on the subject if they were to lay out a set of lifts that compared to the average sedentary man would prove the lifter to be strong enough as to distance himself considerably enough from the common man to be considered "Strong" in general yet perhaps not particularly strong in several lifting circles opinions.
I'm running on here abit, but there is one thing I can say and that is that strength and size do have a pretty solid relationship provided the person eats an adequate amount of food to drive muscle growth.
I have known maybe a dozen casual bodybuilders(aka lifestyle not competitive) that were very decently sized and built in the range of 205-230lbs in attractive condition and not one of these guys benched any less than 275lbs for 8 reps and the average seemed to be around 315 for reps to have a considerably muscled upper body particularly in the chest, shoulders and triceps.
This is just one particular lift emphasizing a few particular muscles, but this observation has been pretty damn spot on from what I have seen from typical gyms in the past 17 years.
I have not seen one guy that could bench 405 for a decent raw rep in person that was not pretty damn big. Granted, I have seen several guys on youtube in the range of 195-215lbs bench this much, but these guys are typically genetically quite abover average at least in the upperbody. "Most" guys that have gotten strong enough to bench 405 or more raw have developed considerable muscular bulk to press that much weight up.
It's very easy to say oh man 405 is nothing, but only someone significantly above the genetic average would make such a statement. I have known a handful of hardworking powerlifter's over the years that were genetically average and in some cases below average on the bench press(often related to arm length/narrow shoulder girdle) that will never bench that much even in a single ply shirt.
Anyhow enough rambling from me.