This choice boils down to how knowledgable/selective one is about beef.
Those who really appreciate a choice cut and do both places will immediately realize Shula's is in a completely different league. That's not to say Yachtsmen is bad, just that it is not of the rarefied quality some think (when compared to the flat out, no-holds-barred realm of top, top shelf steakhouses one experiences upon entering Shulas).
All that stated, I'm not sure the additional quality of Shulas will be fully appreciated by children and young teens - which is something the OP may want to take into consideration.