Initially I was going to toss your experience with UDK mods out the window.
My logic was that employers seldom know of any mods, so showing off your mod would do no good.

But then I remembered that the one game I am playing now (Monday Night Combat of Kirkland, WA) is made off Unreal Engine 3 and their hiring page requests experience with Unreal Script and the likes.
Therefore I conclude that UDK experience can be valuable, but only if you have an idea as to which company you would like to join. Many companies will not appreciate your UDK experience, but there are some who will value it, especially in Japan. That engine has gained a lot of popularity here, but you will need to speak Japanese to be an asset.

Aside from that, I would recommend a hybrid approach, simply because you never know what you will get and you need to broaden your horizons to maximize your chances.
Use your spare time as well as you can to:
#1: Make a completed game using Unity 3D or Unreal Engine 3.
#2: And make your own projects from scratch.

The best chances for the start of your career are small companies, and they are seldomly looking for engine users. To impress them, you need to be able to make a game from scratch.
Meanwhile, if you have engine experience, you can apply to some mid-level companies and hope you get lucky.

Being able to code your own game from scratch is not only a safe-guard, but it also helps you to obtain a stronger position within your company. It should not be overlooked.


L. Spiro

Drk, you should make whatever portfolio project you are most interested in. Seriously.

If you start from scratch you will not want to make an engine. Just code the game and get some results that look nice.
Of course feel free to code a mini-engine. A small library for managing models, a small library for managing 3D rendering, etc. Just don’t add anything that is not directly needed by your ultimate goal.
The point in making something from scratch is to show that you have knowledge of coding and inner game workings, but also that you can complete what you start, so you must be able to finish it in a timely manner.


L. Spiro

I have game ideas that I can make in either engine and I'm not sure which engine would be the best to specilize in at the moment, which would be the best to learn

It doesn't matter. You should read the For Beginners FAQs on "what's the best engine."
Don't try to live your life to satisfy someone else's wants. You'll never succeed.
Live your life to satisfy your own wants. You'll always be happier that way.
Make the game you want to make, using whatever engine suits your own needs. You'll enjoy it more, so you'll do better work, and it will show.