I would generally say that, all else being equal, the therapy that's most likely to be helpful is the one that the person feels most optimistic/positive about, or drawn towards.
A fair chunk of what can be helpful about therapy is the feeling that it's possible for things to change, and for the therapy to be something that can help you with that — and, assuming it's with an actual human therapist, the fact that you're teaming up with another person with your well-being as a common aim (i.e. the therapeutic alliance). Going into the therapy with the belief that, if you fully participate in it, this is something that has the possibility of helping you improve things, is tremendously powerful in itself.
So if, with the info you have available to you, you think that right now, CBT is more likely to suit you than counselling, then I would go with the CBT.
And if it turns out not to be what you hoped or expected, or it doesn't work well for you, there's no shame in that and you can try something else. Or it could be that the problem is not CBT itself, just that the therapist is a bad match for you. This is looking ahead a bit, though — lots of people do find it really helpful.