In terms of pure name awareness, it would definitely be the Dalai Lama.
But in terms of high regard, I think Aung San Suu Kyi is more universally respected - unless, of course, you happen to be president of Burma.
I agree that a no-holds-barred compassion-off would be the best way to decide this.
Two Buddhists enter...and actually, two Buddhists leave.
Gain and loss, status and disgrace,
censure and praise, pleasure and pain:
these conditions among human beings are inconstant,
impermanent, subject to change.
Knowing this, the wise person, mindful,
ponders these changing conditions.
Desirable things don’t charm the mind,
undesirable ones bring no resistance.
His welcoming and rebelling are scattered,
gone to their end,
do not exist.
- Lokavipatti Sutta