[Aesopian]

One thing to consider is what you mean by "intense" and "relaxed".

You can be "intense" by muscling moves, straining, fighting out of everything, being brutual, etc. Or you can be intense by pushing the pace, staying ahead of them, not letting them establish control, preventing attacks and defences before they are a major problem, actively working out of bad positions, etc.

You can be "relaxed" by just waiting for them to do something, only capitalizing on their mistakes, not working to keep good position or posture when you're losing it, etc. Or you can be relaxed by keeping your composure (especially in bad situations), only using as much effort as needed, not getting frantic, knowing when to give up on a failing technique and move on, etc.

So it all depends on what you mean. I don't recommend the first way of being "intense" because you'll just stop yourself from learning good technique. I do recommend the second way of being intense since it'll help you have some "game" while you're developing your fundaments and rolling with guys better than you.

Likewise, mistaking "relaxed" for "passive" or "motionless" wouldn't help you either since it too can lead to sloppy technique and bad habits. But I think it is VERY important to learn as soon as you can how to keep your wits about you in bad positions and intelligently work out of them, and not get so excited when you're doing well that you start making mistakes.

From my experience, most beginners need to work on being relaxed first (whether they do it in the best way or not) because they've usually got more than enough "intensity". This is usually hard advice to take at first, since they're still thinking "How can I relax when I'm always getting beat?" And I don't really have a pat answer for that. I just know that enough mat time and experience will sort it out for them once they decide to give it a try.

I've found that I go back and forth through cycles of being too relaxed and too aggressive. My game starts declining when I go too far to one extreme, and that it's best when I can strike the right balance. I'm constantly jockeying these factors as they rise and fall, and while they'll maybe never stop fluctuating, it is through this process that I've experienced many of my improvements in training.