This is a very deep question that has several aspects to it, and can branch out to very many sub-topics if taken in the right direction.
Taken in the wrong direction–and you can bet that it will on these forums, since there are both people who are bent on provocatively stating outright that Chabad is the best etc. etc. better than all the others etc. etc., and people who are imbued with hatred towards Chabad, as I say you can bet that on these forums it may very well be taken in the wrong direction–it will very quickly (probably about a third down of page one all the way to page 24) spiral into an endless bickering about how Chabad is kofrim, changing minhagim, egotistical, but all the same do good things for the benefit of klal Yisroel…etc….etc…etc…
It really pains me that literally thousands of volumes of very deep knowledge have been boiled down to whether Chabadniks sleep in the Sukkah (a minhag they have kept for hundreds of years, alongside prominent Litvisher figures who had nothing to say of the matter) and whether they eat before davening or not (something which has a very clear heter in the Alter Rebbe’s Shulchan Aruch–and you can see his sources there). Of course I’m going to be required to provide sources, be questioned on what I mentioned, but I have no intention of starting any arguments here, just for the record, so don’t anybody expect any responses on these issues.
Regarding what you ask…The Lubavitcher Rebbe himself asked the Previous Rebbe of Chabad what are the differences between Chabad Chassidus and Polish-Galician style Chassidus (so you see how complex it is, here is a question only with the differences among other Chassidim, and you’re asking about general Judaism!). The response was a very beautiful one, printed in his letters and translated and collected in English in a series titled “Branches of the Chassidic Menorah” by Sichos in English publication (two volume series).
As an introduction, the Previous Rebbe clearly states that he will not respond to the differences between them since (and I am paraphrasing from memory) we don’t have tools large enough to measure these two mountains against each other. As such, he proceeds to explain what made Chabad Chassidus unique, rather than discussing it in contrast against other groups, since we want to preserve and be proud of what we have, and there is no need to compare to others.
This, I think, is a very proper approach. What Chabad Chassidus, then, might have which others don’t (and this is really off the top of me head just so I go away actually having answered your question) is a very practical school of thought which allows one to appreciate and mamash grasp (intellectually) spiritual concepts in a way which ACTUALLY changes one’s life, whether in avodas hamiddos, in our Torah learning, and..well our entire avoda in general.