I went to a small liberal arts college and worked at a large university lab, that had undergraduate interns. From both experiences I agree that it is the lab and not the school that matters. However, there are conditions that you will be more or less likely to find, depending on the type of school. In general liberal arts colleges will give you more personal attention and large universities will have more resources. Funding at liberal arts colleges is focused on undergraduate education and funding at larger universities is focused on research.
Liberal arts: A lab is led by a principal investigator or PI. Liberal arts colleges often do not have graduate students or have few graduate programs. So, at a small liberal arts college you will work closely with your PI and get to know them well. I left my college with great letters of rec that helped me overcome a poor GPA (due to a medical problem in my first two years) and get into grad school.
University: The undergrads were trained by PhDs and post docs and had little contact with the faculty. Post docs and PhDs can often be great teachers, though, since they either are students or were students recently and might be able to anticipate the student's perspective. At a university, they will normally write your letters of recommendation and the faculty will sign them.
Liberal Arts: All of our grants were training grants, so the emphasis was on teaching, as opposed to producing results. This means you will get to do more independent work. I got first hand experience with the equipment (EEG) and techniques (analysis of FMRI and EEG data) that few undergraduates get to use. Additionally, I know of at least two of my friends who published, as first authors, in major research journals. This is not uncommon in my school.
University: The undergrads had to learn a program that is no longer used by most labs in the field. There was little room for mistakes (all of the labs grants were research grants), so the undergrads were given the task of modifying previous work and really did not develop any understanding of how the program actually works. However, this lab was an older lab. I also believe students at an older lab at my undergraduate school had a similar experience, where the methodology they were taught was not consistent with current standards in the field.
They are pretty equal in this area. Liberal arts college professors often collaborate with people at larger institutions and can connect you with other labs. I have friends who got summer jobs at Stanford and CalTech this way. At the large university, one of our undergrads got to go to Oxford for the summer, because of the professor's connections to a lab there.
Equipment and Resouces:
Liberal arts: We did not have access to some of the most expensive equipment (an MRI, for example). However, one of my professors also worked at a local university that had access to an MRI and we got to use it there. Ideally, you should get some lab experience at a major research university, so you are exposed to techniques that require more expensive equipment. You can do this during summer internships. Getting more experience at different labs will look good on your application.
On that note, a liberal arts college is more likely to have grants that will help students study at other institutions. My college had several such grants for student research grants. Additionally, all senior thesis was funded by the department. The senior thesis funding and one of the summer fellowships both require students to focus on their own original ideas. In most fields the first author is the person who had the idea for the project. This is how undergraduate students were able to become first authors.
University: Universities will have the best equipment, but they are less likely to have funding for student research. The institution I worked at had grants for students, but they were only for work at that university. They also had no specific grants that would allow students to propose their own projects, based on their own ideas.