No company will hire you if you ever say this...
Big company is normally for people who seek for laid back environment, especially for fresh graduate. Because the projects or any being assigned is split as according the skill set. You would most probably end up become a support type engineer until you managed to be independent without the need or least of supervision. There is no shortcut.
Small company is preferred their candidate to be 'Can Do' type. Because they are well independent and able to manage multiple projects by themselves. A well manage time management can survive this, otherwise you will end up being a joker within the company.
Nope, you cannot be consultant if you are not those outgoing type of people. And, a consultant required experience up to 3-5 years or your learning experience that is consider on par with any seniors. Consultant required high knowledge of such technologies being used, understanding the flows that is used in the minimal provided time frame and provide support for your clients.
There is no shortcuts. Don't think of how you gonna be like in your future, it's not gonna happen if you don't improve at present. I not trying to be harsh but by experienced. Any certificates you have are all just for decoration despite Degree holder, Master holder etc, they are nothing, because a true employer will only judge as per your learning experience and not certificate or working experience.
As mentioned, assume the candidate A with 5 years of "Working experience" vs the candidate B with 2 years of "Learning experience". I bet you can't see what are the differences between them. You can laid back, slack or anything that counts as "Working experience", and the quality product that delivered is low is still count as "working experience". A learning experience that is to judge a candidate that has the value to deliver quality of products within the shortest time frame possible, by bring a good profit revenue to the employer despite the candidate with lower duration experience.
The example above is how you should be like in future. For now, i would advise you, regardless any amount your receive whether or not high or low. You will need to have a positive thinking mindset, a fresh graduate is like a blank paper, any learning is your experiences, so start from there. Once you have the skill set that you think that you are good to go, that is where you can seek what you actually want in future.
....Back to the point, which type of company can enable me to learn better ? It seems that if i work in a big company , i have limited things to learn since you said that i will be assigned to certain part of project only, am i right ?