I worked in both SME and statutory boards previously. Here's some of the lessons that I learnt. It may or may not be relevant to you but here it goes.

1) pay aside, if you are a fresh graduate, statutory board offers better exposure and helps you fine tune what you want to do later.
2) the downside of joining statutory board is that it might numb your ambition to join the private sector later as there will be other life commitments along the way (like marriage, kids etc) that changes your priorities. Not necessarily bad, just a matter of trade offs.
3) SME will never offer you the kind of exposure and training as a young graduate. for mid career, it might make sense as you can apply what you learn immediately.
4) for SMEs, it is all about bottomline. So it is about sales, P&L. unless you get to share the upside in the company, I would discourage you from joining. In another words, your pay is tied to how much you can contribute to the company. the reason they will cannot pay you as much is that every cent they pay you eats up the bottomline. However, are they able to share the upside if the company do well?
5) you can always move from statutory boards to SMEs, but not the other way round.
6) join an SME where you are a linchpin in the whole business. if you are indispensable, it helps. Also, do you know they founders well？ for SMEs, you only need to get along with the founders.
7) avoid family-type business where the founders put his own 25 year MBA son as CEO.

I hope the above helps. good luck.