Over ice cream today, there sparked off a tiny piece of debate that is still ringing in my mind while I am typing this through. But, I wanted to collect my thoughts regarding this and then present the matter. Well, I guess instead of a comparison first, I think I will present the facts on each option and then move on to a comparison as a summary. A Small Company:Everyone generally knows the "advantages" of joining a small | medium sized software firm. Let me enumerate it just in case
 You grow with the company.  You get _recognized_ fast [I will present the counter-arguments for this later].  If it's a good enough organization, your growth will be faster.
What I perceive: Joining a small company may not be as simple as it is. How I would put it is a big gamble. The first being the reason as to why that company is called a _small_ company. A company can be small based on
 Strength of its workforce.  The diversity of its verticals.  Maturity of the company.
The best part about "small" companies is that they _grow_ [well they HAVE TO in case you want to be associated with a _good_ company]. I am talking of a growing company - growth defined in terms of
 Number of projects coming in.  Number of people being used by the company.  Maturity of the company - "thinking like a small company even though they are edging to become a big conglomerate" [quoting Jack Welch].
Only if you are in a "small growing" company would it be advisable for you to stick with it, especially if you are considering a "job"!
The reason as to why people say that they are _recognized_ faster and that their _growth_ is faster in a small company is simple enough. Being a small company, they don't have many people. Consequently your karma and charisma will reach bear itself on the top level very fast. Now here's where the trick is. ONLY IF THE COMPANY IS GROWING, will you be growing faster. If you are asking for justification, here it is
 Small companies, unless they have enough projects coming in CANNOT and usually DO NOT post you to a leadership role for the simple reason that they may not want to shake the balance. Even if the PM [Project Manager] isn't as charismatic as you, he's PM for a certain reason and the company isn't certainly going to change him, especially since he's delivering.  Your charisma and karma could come out as a threat to your immediate superiors who are also in this rat race. Consequently, your pressures may just build  If you would notice another thing, if the company isn't _growing_, then you are in a soup, as your growth would also be equally stunted =). This is especially the case, if it's a products company.
That last point is why I would say that joining a small firm is a gamble. Coz it could bring home the mother load, or it could force you into the job market sooner. It's EXACTLY what you should do, if you are up to it and want to make a jump start to a promising career in any field. Because making a mark is easier amongst 2,000 people over 32,000 and more ::blushing. Please note that this is NOT a sign of meekness. It's smart thinking what exactly you want from a career that should make you determine joining humongous giants of the industry like TCS, Infosys, Wipro having over 30,000 people on the average on their payroll, or the smaller variants who are bound to grow coz of their wonderful product, fire in the belly drive to grow, and their overall effusiveness to just struggle and move on.
Another reason why I one may like a small company is that you soon get close to the 2,000 off people you work for [still is a huge number]. Along the same lines, a large organization might just be what you need if you are missing the large crowds and dance parties ;-)!
In the end, it all boils down to one actually. What do you expect out of your career at any stage? Masti @ work, think innovatively and try to implement them in your work place, enjoy your ass by a late night session of brain-storming as to why the hell isn't that problem getting solved with your teammates over pizza, and generally a less structured, more informal work culture? Then I think that is found more often in small companies. At the same time, if you are taking the more traditional line of a "job" and don't mind taking the "usual path to stardom", usually a long drawn process that is FIXED, but enjoy time with a lotta people, and generally are ready to put in long hours, coz it's expected outta you and comes with the job description, work in HUMONGOUS offices with large amount of recreation [even an open air auditorium ::whoa], then you are looking at a large organization.
Note: I have not discussed about the pay aspects of the companies. Generally you are paid better in a small company, and often it's based on your performance, evaluated in terms of profit that it fetched to the company. There are other aspects that accompany this as well viz. how you might be paid as well. =)! Right now, I have to get back to getting bored so I will take a break from typing. I will have to reorganize my points on this as well and so I am expecting a rewrite of this soon.!