Changing Hutches - will they fret?

Hey, I'm new to the forums so sorry if this has been mentioned millions of times.

We recently rescued two male rabbits and they live outside in the back garden in their hutch. It's a double decker one but without the ramp, as they kept fighting so we had to give them their own level. We have two seperate runs, which we put on grass and patio (depending on weather).

But we want to give them more space in their hutches and my mum wants to know if they'll be alright and will feel safe in a new hutch?

The new hutches we're looking at look something like this:
http://www.zooplus.co.uk/shop/rodents/cages/rabbit_hutches/natura/14642
but with a floor so it's not open to the ground, and we keep picking them up to put in their runs.

Or something like this one:
http://www.zooplus.co.uk/shop/rodents/cages/rabbit_hutches/accessories/33224
But if we got this one, would we put it on patio or grass?

Bearing in mind we have 1 dog and 2 cats. The dog is fine with the rabbits, it's the cats that get a little playful, poking their paws through the fencing!

So would they feel safe in a new hutch?

lol, did any of that make sense?

Hi,
You need to be looking at hutches which are 6'X2'X2' to give your bunnies the space they need. Are your bunnies neutered? as if they aren't that might explain the fighting.

When you move houses with them just keep everything smelling like the buns. Don't wash any toys or empty the litter tray that day so they know its there new home Within a couple of days (or probably quicker) they will get the idea :lol:

Spice used to sulk for a day or two when she moved home, but as soon as she felt safe again she was fine. Her last move was just her set-up moved from house to garage. Nothing changed in it and she never showed any signs of sulking this time

When she sulked it was just sort of looks, like she wasn't as happy lucking as normal because she was unsure of her new boundaries/levels/territory. She was always back to normal after a day or two. (She carried on eating/drinking/pooping etc like normal so watch out for signs of change with these things).