You won't find too many differences other than some changes in the Nusach and the siddur.
Most MO shuls tend to be Nusach Ashkenaz from what I've seen, but you should inquire. That's not a given rule. I don't recommend bringing a siddur with you unless you are personally comfortable with the Koren siddur and can't readily transfer to another one. My reasoning:
- The shul has its own siddurim usually in ample supply, so there's no need to bring your own
- If the shul is not in an eruv on Shabbat, then you definitely should not bring your own siddur
- You may get confused with finding the proper page that the cong. is on if you use a different siddur than the rest of them do
The tunes the cong. sing may or may not be familiar to what you’re used to. It depends where you go. Some do more congregational singing than others.
MO shuls tend to start much earlier than Chab"d shuls on Shabbat. In the U.S., that time can range from 8 - 9 AM in most places. But, it's most likely not starting at 10AM as many Chaba"d shuls do.
If you're a guest, you may or may not find the "open friendliness" that I've found Chaba"d tends to offer. Some MO shuls have people that will spot you as a guest immediately and you may get numerous lunch offers. Others, have no clue that you came in or cared either way. Pick a "small" place, if you can. It will be a less intimidating start.
I will say that MO shuls have changed significantly since the 70s. In U.S., it seems that philosophy and demographics have trended towards being halachically stricter. Many men in MO shuls wear black hats, now whereas that wasn't as much the trend until about 20 years ago. I've seen a bit of a trend towards separate men / women seating at meals and even at lectures. My point is that there's no set "standard" - at least less so now than there was 30 - 40 years ago.
(If you're somewhat curious about the MO trend, Rabbi Riskin's Lincoln Square shul in NYC was considered MO when he was there. I don't know if it would still be considered that way, now. Even so, I understand that it has attracted more of a "yeshivish" crowd.)
In short, I recommend contacting the shul's rabbi and asking some basic questions and introducing yourself. It will provide you with answers and it helps if the rabbi, at least, knows that you will be a guest there. It also makes it easier for you vs. entering "blindly".