As a programmer do you recommend learning Android or IOS programming, or just learn PhoneGap?

All Android and iOS applications are mainly developed in Java.
PhoneGap is just a tool build basic, cool level native applications written in HTML, CSS and JavaScript.
When you finally build the application all codes you have written are translated in Java programming language.
But if you want to develop data driven application or native application based web application then PhoneGap is of no use.
You must know the Java to program those applications.
You can also use third party tools such Adobe FLEX to build data driven applications and this does the same as PhoneGap,

PhoneGap is good Tool used to create application used in multi device , to be more specific for platform you have to learn , also i think it depend on your background in programming , if your background in java it will be easy to learn android , also depend on the market you want to target

You need to learn both but start with android or IOS.

@Jasmin Ahmed -- I didn't understand how you come to know that iOS apps are mainly developed in Java?

For iOS (iPhone/iPad) developement, the native way is to use Objetive-C on XCode. No room for java at all. However you can use java on third party tools that have been use to devolop hybrid mobile apps like Titanium, Phonegap or Xamarin. But at least,  as far iOS is, be clear that all actually atc as intermediate between native frameworks combined in iOS and them. They actually generate high level Objective-C code to interface APIs declaried in those frameworks assuring everything in compiliance with the Apple Guidelines.

 

Basically if you want to be a core programmer who don't like barrier just go for Objective-C/Xcode for iOS and Java/Eclipse or Java/Droid Studio etc. for Android development.

However if you would like to be a seasional or prefer scripting language or want to develop enterprise apps without worrying about some low level code go for Titanium (Appceleretor) or Phonegap.

 

For C# developer choices are Monotouch or Xamarin. In fact there are more like Application Craft etc. that support different scripting language that let you build apps without writing much code however with limitation in using advance features.

 

It depends upon your interest and your proficiency in language, java and objective c in this case. I've worked on both android and ios and I thinks that both of these platforms are very interesting and teaches you good programming practice. However I think android lags behind from ios in couple of things, like you need to create views of different sizes to cater different android devices. Objective C, the language is not verbose like java and very readable and of course it supports pointers. Phonegap is an amazing technology where you can create hybrid applications, which can run on multiple devices. You can use it to consume web services, design appealing UIs with css or sass, use several libraries of javascript, etc. However as it works in webview, it has its own pros and cons. You cannot use it for heavy calculation purpose or if you're too much worried about memory management. Phonegap doesn't support all the APIs which is provided by the SDK but still I think it's a attractive technology and lots of enterprises are using it already.

phonegap can be used for cross platform, when your has only web service based fetures and UI related apps.

If your app has audio/video calling voice mail features then phone bad is the bad option to choose.

Let me put it in a simple manner. If you are working in the US ,Uk or Europe , I would recommend you learn iOS. Else Android would be the first option. Now with the best increasing number of programmers... Learning both these Technologies is actually a must. Now when it comes to phone gap... It is very useful since it covers hybrid app development. This can be learnt alongside Android or ios,so u can always have this option.