I had enquired on some institutions for internship courses, they have offered me an 6 months training support on Front end training and most of them are using Mentor Graphics and Xilinx tools only. They told in Front end there is Designing and verification part are available, so in that which will be more reliable (Designing or Verification).
Both options are fully independent career options. I know some people treat verification as a 2nd class citizen to design or that verification is just a stepping stone to design. However from my experience, demand for verification usually outpaces the demand for design. It's always in the critical path and it only gets worse as designs get more complicated. Innovation to speed up verification is VERY VALUABLE.
On top of that, the best verification people that I know chose verification as a career and not a stepping stone to design. Those people are very well rewarded and I believe their accomplishments is tied to that mindset that have for verification. But it's definitely a "it depends if you like it, and liking it sort of depends on whether or not you're good at it".
I don't suppose the course/internship has some sort of rotation program so you can get a first hand look at which one you like to do better? Your career isn't set in stone but at least in the short term, you can try to secure a job doing something you like to do.
<--- not a professional counselor