I, too, was thinking night terrors when I read your posting, although it's hard to say. Some children are a little overwhelmed by the openness of a bed versus a crib.
I had 2 children go through night terrors, and it is really something you have to have patience to work through calming your child until he or she settles down enough to go back to bed (afterwhich they will fall immediately back to sleep, since they were never fully awake). If your child is alert and cognizant of you and his surroundings when you go to him when he is crying, it is probably NOT night terrors, just nightmares. When kids have NT, they may seem awake and respond, but they will not be totally aware of where they really are and may still be living their nightmare. They are only semiconscious of you, their surroundings, and circumstances.
If it is just nightmares or anxiousness about his new open access bed, you must be his strength and help him overcome his "fear". I'm sure you've been warm and loving, but ultimately, he needs to work this out on his own, and that means in his own bed. You can help by making sure he goes to bed under the best of circumstances: share a book, talk about night, and give him something to look forward to tomorrow. Sometimes, you need to get creative. Our oldest was 3 when he started, and big into Ghostbusters. My husband made a "trap" to catch all the bad dreams, and that was the end to his crisis.
Our second oldest had NT and we tried a lot of things (before we knew what we were dealing with). The patient, calm recommended technique did not help, though. Bright lights, firm voices, and a cold drink were the fix to break him of his state (which took 5 minutes as apposed to 20 or 30 waiting to calm him). Then, he would go to bed and sleep the rest of the night away just fine with no memory of his outburst.
Our third, our little girl, would only get NTs when she let herself get too hot at night. We dressed her in appropriate pj's, but she loved to snuggle under her comforter. Most nights, she slept too soundly to push it off of her sweating body, and it was those nights she would have a NT. I put 2 and 2 together and since I make it a routine to check on her 30 minutes after she goes to sleep to pull off the comforter, she has not had another NT episode.
Our last little guy (now 5), thankfully, has not had either!
I think your son may be more likely having anxiety about his new set up, since he is aware of your presence in a very real and coherent way (otherwise he wouldn't know you were there and not care if you left). You need to let him know it's okay to call for Mommy or Daddy if he wakes up and is scared. It's okay for you to go to him to calm him (and keep him out of your room), but then you need to tell him he's a big boy, tell him why he doesn't need to be afraid, and that he needs to sleep in his bed just like mommy sleeps in her bed (although this is easier said than done). He will probably cry a bit when he realizes he still has to be alone, but it is normal for toddlers to go through this experience. Night lights, a comforting stuffed animal or blanket are helpful items (plus ear plugs for you!). A bigger bed will not matter, but character bedding might help or some favorite wall art.
Having said all that, it really boils down to your priorities and tolerances, is it more important he sleeps in his own bed or that you all get some sleep? Can you stand to let him work through his fear or does it tug at your heartstrings? Your son will survive, and he will not be emotionally scarred by having to stay in his own bed when he doesn't want to (and without mommy). It just takes some willpower and determination to stick with a good decision. Sometimes our caterings enable more demands than they eliminate.
Still, I admit, I have capitulated at times when sleep took higher priority over keeping them in their own beds, and it is an endearing moment to snuggle with your child... but I paid the price, too.
Good luck!