It's very different.
I like it a LOT better, but I had grown tired of the lack of strategy in civ4.
Here is a very quick overview of how Civ5 is different:
First -> it uses hexes instead of squares (with octagonal movement). This is a big departure from the traditional civ games, but I really like it.
There's multiple layers of timers/counters to be aware of and you need to balance them to some degree to do well.
Social Policies: these are sort of like your old government policies/civics/whatever they were called. It's very similar to the class trees in WoW in terms of how they're designed. You have 8 social policies (some are unlocked as you advance through the game), and within each there are 5 sub-policies, each of which are beneficial in some way. Once you accrue all 5 policies in a group, it counts as a 6th policy which is usually pretty good. These are controlled by your culture; more culture, quicker policies. Policies cost more as you accrue them
Tech: This is pretty similar to the old tech system from civ4-3-2-1. Certain techs will reveal resources on the map (and using the add on I like, it gives you the ability to see the resource before you can use it so you can build/conquer with future resources in mind). Techs also represent the major epochs: Ancient, Classical, Medieval, Renaissance, Industrial, Modern, Future. Each of these unlocks more social policies as you get to them.
Happiness: Your empire needs to be happy for it to grow. Happiness is basically a way to control population. Population is also the biggest source of unhappiness, with citizens under occupation/in puppet states costing you more happiness than those integrated into your empire as citizens. If you want to have a large population, you need to have a lot of happiness. happiness comes from buildings, luxury resources and from things you unlock as social policies (i.e., +1 happiness for each specialist; +2 happiness for each wonder, etc).
Money: This, again, works a lot like the old civ, except that if you are out of cash you don't get any science (maybe that was in the old one too?). There are a lot more money-making options and they've done a good job (at least the mod has) of making the oceans a better economic resource.
The combat system is really cool. You can only have 1 unit per tile & there is a unit limit (based on the number of cities you own -- I seldom run out unless I'm preparing for a conquest victory) but all that cap does is just slow down production of future units. There is a better rock-paper-scissors balance between units now. Ranged units are good to use to soften up units, but are trash on defence. Early melee units are good for attacking/protecting, but can get beaten by a handful of other units pretty easily. Vanguard units have a defence bonus, are cheaper and are good at absorbing damage, but are crappy for going offensive. You no longer need transports, every unit transports itself but is easier to kill while being transported. Naval units are nice ranged units; once you get to the modern age and start being able to bombard 3 tiles inland, they are VERY powerful. Aircraft are cool as well -- more options to shoot down enemy fighters and whatnot, but I find the AI can't manage their planes that well, so I don't usually go far down that path to keep the game more interesting.
Cities: The days of the infinite city strat are over. you can just keep building/conquering cities indefinitely -- that is still a strategy -- but the happiness + social policy penalties make it more economical to balance your empire. I typically build 4-5 really strong cities and fight for the land to let them grown, rather than just trying to build a TON of cities. Based on how the game is balanced, you can go for a LOT of small, crappy, focused cities (each one with a specific focus -- cash, tech, production or culture)
Great People: One for each major aspect of the game (artist, scientist, merchant, engineer, general). These guys work like the previous game, but the general is actually more useful (military modifier for units within 2 tiles) and there are ways to interact with enemies (making yuor artist take over all tiles within 2 tiles of him -- even if they are owned by others) or city states (merchants can conduct a "trade mission" which will increase their opinion of you + give you a bunch of $$$)
City states: these are cities that are standalone, not attached to a larger empire. they will ally you and provide bonuses (military - gives you troops regularly, culture - provides you culture, and farmers - export food to you).
Barbarians: I find barbarians a huge pain in the ass in this game. They are always around trying to steal your settlers and rush your cities early on. They don't really screw you up, but they are better than in previous games -- especially when the AI sucked more.
Trade routes: in this version, trade routes are actually defined and give you extra money based on the population of your capital + each city it is connected to. it makes having control of your capital even more important.
wonders: there are a lot of really cool wonders
The endgames are all pretty much the same, so I won't go into that.
That's my 'quick' review/what's new post for civ5 :p
PS. everything I mention assumes you have this mod installed:
http://civmodding.wordpress.com/
I consider the game unplayable without that mod; it shouldn't have shipped as vanilla. the game wasn't properly balanced and the AI had glaring holes where it would suicide on someone or launch failed invasions of city states over and over again.
PPS. there is a colonization addon or something for either civ4 or civ5 -- i saw it in the store a while ago.