Because of the way the business side of engineering seems to work, many smaller SE firms generally deal with the same clients and may not get exposed to a great variety of work. This can work well on the economic side of things for the company, but can get a little boring for the engineers. And with the economic situation, boring is not bad as long as it pays the bills.
Interesting and exciting projects are sometimes luxuries for structural engineers, at some point to become as economic and profitable as possible most companies come up with lots of templates and things to make your job easier, but maybe more mundane. Computers further remove some of the challenges on the computational side of things. I think this would be even more true the larger the company, and you may be asked to specialize in a specific area or division. A small to mid-size company, IMHO, will offer you the opportunity for the broadest range of projects and materials. It also depends a LOT on your boss and his goals, his contacts, what he envisions your company doing. He may be with status quo and just happy riding it out with a few safe clients that don't result in too many head turning projects but always pay their bills (his goal is to make money and not make your job interesting)...
A larger company may offer bigger and more high profile projects, but I think bigger projects have the tendency to get split up into lots of pieces and you may only be involved helping a project manager with one portion. But maybe that is what you want, so you can work your way up into their position and be the lead engineer on big projects. I've been there, and that can be enjoyable too.
Personally I prefer small to mid size projects that I do mostly myself with input from other engineers as needed. I prefer a lot of variety and don't want projects that go on for several months, if they can be avoided.
Then one day you could finally get that super challenging project with an uber creative architect, and all it ends up getting you is gray hairs, long hours and less sleep
You have to find out what works for you, and no parent, buddy, mentor or random guy down in Florida from a message board can lead you there. You have to find out what makes you look forward to going to work every day (or at least not grimacing at the thought on Sunday evenings). To me it is all about balance and in no particular order:
-geographic location
-bosses and coworkers
-money and benefits
-type of work
-career opportunities / ability to advance
-independence
-hours (regular 8-5 or every other weekend against deadlines?)
And these can all change, they have for me in my life and career. Right now I am about to start a family and am still concerned with the econonomy- so I am OK with safe, stable, regular hours, decent pay type job.... Plenty of other ways to seek out excitement outside of work for now.
If you are in your mid to late 20s, which for some reason I get that vibe, and are not too tied down with responsibility, look for a job on the opposite coast or in a slightly different industry or in another country, why not? You have your whole life in front of you, and you are not sure what you want.
Or if you can swing it and MAN I wish I would have done it, sell everything you own and go see the world for at least a year or as long as you can afford it. It will open your eyes in ways you have never imagined, and likely refresh you and help you figure out what you want to do. Even if you have travelled or lived in another country, pick a new part of the globe and get out there and out of your element. Go someplace with weird foods, different languages, and at least a few places that are less financially blessed as the US.
At the very least, you will have gained some valuable perspective, and perhaps even that same job (or similar) will become a good place to hang your hat while seeking out other new adventures. You may discover you have one of the most interesting careers out there in one of the greatest places in the world!
(off my soap box now, good luck my man with your life decisions)