Try them all :D

indeed, all 3 are primarily shooter engines, so see which one tickles your fancy. You'll be spending a LOT of quality time with it. <g>.

I am going to do a 3D Adventure RPG for PC (Windows 7) by myself as my first game

Co-co-co-co-combo breaker.

On-topic:

I would go with unity, it is far more popular in the indie scene, so you are more likely to find more help. But you should probably start far smaller than a 3D RPG.

Ehm, unity isn't far more popular. Actually in my opinion you should decide between Unity and UDK. Crysis is actually primary a shooter engine. But UDK and Unity aren't for sure. Both can be very easily used to create any game you want. UE3 got the award for the engine of the year. And in UDK you get all the features of UE3 except of native code acces. And in unity, the free version is a little bit limited. But in unity you can script in 3 languages(but you will propably use only one anwyays). So I advice you to try out both and choose. I tried out both, but like UDK more. Also, both engines have a giant community. And you should start with something smaller than a RPG.

I said it is more popular in the indie scene, at least in my experience I see far more people using it here than UE.

indeed, all 3 are primarily shooter engines, so see which one tickles your fancy. You'll be spending a LOT of quality time with it. <g>.

Sorry, but though the first two are more geared to shooters, Unity is NOT. It is true that shooters have been made with it but it is made to be much more general and so you don't have to "bend" it to a given genre like you would with UDK and the Cryengine.

But, the rest of the quote, and pretty much most of what else was said I agree with. Unity is more commonly used in the indie world from what I can tell, and the UE3/UDK seems more used in bigger teams and commercial studios. I'm leaving Cryengine out of this as I haven't seen any evidence that it is capable of much more than FPS games, while the UDK, though meant more for the FPS genre, has been used to make other game types, and Unity much more so.

UDK Pros: It is very powerful, if not the most powerful engine available to indies for free(or very cheap, relatively speaking). If you are non-commercial, it is fully free, and for commercial usage you pay $99, and then after you earn $50,000 you begin to pay 25% royalty off of your earnings. This has been the center of controversy in many topics, but many would consider a good deal considering what all you get with the UDK.

UDK Cons: It is relatively difficult to use, though once you learn it, your opinion of that can change. The currently used language(Unreal script) isn't used anywhere else, and if you spend the time learning it now, you MAY feel it was a waste once they switch to C++ with UE4, assuming that they make a UDK for the new version, which I believe is likely. This also depends on how long it takes for the UDK4 to come out assuming it does. Also, as compared to Unity, the art pipeline for indies can be more difficult, as most of us don't have access to Max/Maya, and I've seen varying topic posts as to how easy/hard it is to get assets created in Blender to import into the UDK. Lastly, the 25% royalty is pretty steep. This may not break the deal though, because you would think that if you ever make 50,000 with it, the 25% won't hurt anymore. But compared to the price of Unity Pro, it is suddenly more expensive as you make more money, while Unity Pro "only" costs $1500 for just the PC ports.

Unity Pros: Generally, it is much easier to learn. Also, the 3 scripting languages are much more "known" than unrealscript. C# can be used outside of the Unity engine, and Unityscript is "similar" to javascript, while Boo is "similar" to Python. Also, the free version can be used freely, without even paying $99 to use it to sell games with, as long as you don't make over $100,000 in a calender year. Also, from what I have seen, there is a much bigger community around Unity, with many websites with massive tutorial groups. You also get the asset store, which can help get things started. Also, it works very well with Blender, and other modelling software. Last thing, since it isn't geared to a specific genre, it is easier to do some wacky game you want to make then it would be with the UDK, as you don't have to "work around" the FPS stuff, which can be complicated or not.

Unity Cons: Well, the free version has certain limitations, though they have lifted some of them. You don't get full access to the shadow system, while with version 4.2 you can do hard shadows with one directional light, though before you couldn't do any shadows except "projected" shadows. You also don't have access to the "fancy" post-processing effects for the most part. But most of the things you can't do won't bother someone just starting out. Also, as compared to the UDK, the price for the "Pro" version costs more right now, while the UDK only costs $99 right now, though with Unity you never pay royalties, so it is a matter of paying more now and nothing later, or paying little now, and lots more later, that is assuming you actually make more than $50,000 in the first place, which most indies startups never do.