The only way you'd be in psych--or LTC--forever is if you let yourself be pigeonholed. Many nurses have made the transition between specialities. It may not be instantaneous to get out of psych or LTC, especially in this job market, but it's not impossible.
Pick the job that sounds more interesting to you and sign on. I'm personally a fan of psych...and if you think about it, psych patients are everywhere, even in the LTCs
. So what you learn there will travel with you. But LTC is nothing to be sneezed at either, because you will be a master at time management and dealing with older adults when you are done. And in BOTH specialities there will be opportunities for using your medical knowledge, since neither group of patients checks their medical issues at the door at admission...especially if you go for sub-acute, geropsych or psych acute medical.
Work your year, then look at applying at hospital jobs. You'll have a year's nursing experience under your belt, which makes you a better candidate than the average new grad or worse, an old grad with no experience.
Of course, you could also start looking for hospital work before the year is up and if you find it, jump.
I honestly can't think of a con for taking either job. New grad jobs are very few and far between, and the fact that two landed at your feet is something. Either job is RN experience and IMO looks a lot better on a resume than an empty space because you were waiting on a hospital-only job. Look at all of the Old Grad threads here and you will see what I mean...the longer you are unemployed, the harder it will be to stay competitive against the continual crop of new grads.
Best of luck whatever you decide!