<p>The answers you're getting there aren't what I was hoping for, so I'll take my best crack at it here.</p>
<p>The best kind of lab to work in, hypothetically, is a lab that is on the brink of being a very big deal but is currently very small. In that lab, you'll stand a pretty good chance at a major publication, your professor will soon become widely respected, you'll get lots of attention from him/her, and you'll do a lot of very meaningful science.</p>
<p>In addition to being very rare, these labs are basically impossible to discern at this point.</p>
<p>The advantages of a small lab are obvious: more likely to get a meaningful project of your own. Any publications that result are more likely to have your name on them. You'll have good interaction with your PI, who will get the better chance to take the time to get to know you personally and therefore write a better letter of recommendation.</p>
<p>The advantages of a large lab are similarly obvious: you're more likely to be involved with serious research and there's a small -- very small! -- branding factor to it. More importantly the quality of the projects is likely to be very high. While you're less likely to have your name on any given publication, there's a lot more pubs coming out of such a lab.</p>
<p>For the purposes of the letter, that's clear: go to the smaller, less productive lab. They'll have more time to get to know you and write better letters. The big-name aspect certainly does not outweigh that advantage.</p>
<p>For the overall purpose, however, this isn't very clear to me. I'd say probably to go with a smaller lab, where you'll have more responsibility and get to know people better. But you might well be doing less fascinating science and have a harder time pointing to any tangible results and accomplishing anything.</p>
<p>So it's clearly a difficult tradeoff, and my recommendation is very tentative.</p>
<p>Ultimately, I would make the choice based on the personalities of the respective PI's. If you think you can meaningfully get to know a PI, then the larger size of a lab starts to present only advantages and no disadvantages. On the other hand, a cold, overly-ambitious PI might negate the advantages of a smaller lab, too.</p>
<p>So it's a hard dilemma but hopefully this was of some help.</p>