Ideologically, they were typical upper-class enlightenment-era humanists. Not very far off from the French Revolution in terms of initial ideology, in my opinion, and chances are Decembrist regime, if it were established in the first place, would have ended up falling, or being overthrown/coopted by yet another character within the Russian political scene within only a few years. My bet is it wouldn't survive until 1840, let alone 1900, even if successful at first.
Most of Decembrists' leaders were basically, as Midgard said, "..Upper-Class Enlightenment-era humanists." There was two basic camps within the Decembrists Revolt, the Southern Society and the Northern Society, both born out of the mildly-reform orientated Union of Salvation which was founded in 1816. The man that Midgard spoke of came mainly from the Northern Society, a moderate reformist organization based in St. Petersburg. Many got their ideas directly from the reforms of the French Revolution era. Most were officers that had contact with these ideas serving in Europe to help defeat Napoleon and put down post-1815 revolts.
On the other hand, their was also a Southern Society, much more radical and mainly based around improvised landed nobles in Russia's south - although it to had wealthy following. The Southern Society, which also had influence in St. Petersburg was mainly the civilian leaders and sympathizers and was a strange mix of anarchists, demogogues, anti-monarchists and proto-communist/radical socialists along with the usual aristocratic reformers- including a couple of good ol' fashioned rebellious peasants closer to in spirit to Medieval peasant revolts then to modern revolutionaries.
However, most of the prominent leaders were older military officers that had some slight liberal leanings and believed the Constantine would be a reformer and Nicholas a reactionary. If, and it was quite possible, Constantine could be convinced to take the throne and allow for a Constitution - in which Constantine would keep most of the power, but would allow for a very, very weak legislature, think the Duma in 1905. Probably the biggest side-effect would earlier attempts on modernization: codified law system, reform of education, reduction of the privileges of the nobles and priests, limited voting rights, a possible earlier attempted at industrialization, the ending of military colonies and the forcible resettlement of people to the east as colonists and the other worst cases of Czarist absolutism.
Things wouldn't be all rosy and happy though, especially not immediately after the revolt. People like Pavel Pestel and other radicals within the Southern Society would probably stage their own revolt in the South of Russia before too long because the Northern Society's reforms are not broad enough. For a couple of months with vestiges listing for years most of the Southern Russia would be like one massive peasant/socialist revolt with strong nationalist tendencies: nobles being put to death, destruction of monasteries, murdering of priests, redistribution of land, pogroms and other fine things of that nature, basically a mini-version of the Russian Civil War of nearly a century later. Then comes the famine because of the breakdown of infrastructure and the dissolution of farming estates in the southern Russia.
Although both the Northern and the Southern Society had contact with the Polish underground, don't expect an end in occupation of Poland, the Baltic, Finland or anywhere else. The Decembrists had a strong nationalist and Pan-Slavic bent that would be trouble in a couple of decades when they'd try to push in the declining Ottoman Empire and we would get a much more deadly Crimean War - Russia would have started to have some amount of industry and railroads by that point. Also, just because Russia has a constitution don't think anti-semitism would be any less of a problem. The pogroms of the late 1800s and early 1900s will probably get moved up about fifty years and last until there's either no Jews left or the country collapses. As much as the Czar are considered reactionaries they didn't have the kind of populist and demogogic hatred of the Jews and other minorities that some of the German deputies in 1890s did and this would surely carry over to Russian politicians very soon.
