I would feel so much safer on TNG's Enterprise than on the original. On the original, I'd constantly worry about some random whimsical decision Kirk makes might get me killed (in all canons for Kirk, this applies.)
Picard, though--I *know* Picard would want to rescue me! And even if I was the red shirt who gets swallowed by the black lake oil, or the yellow security shirt who gets shot down in a surprise attack the moment we hit the planet's surface, I would R.I.P. knowing that Picard would remember my first and last name, and write a glowing letter of my bravery to my parents, and probably arrange for a lovely wake in 10-Forward, and possibly write my kids recommendation letters for college.