At present, dog laws vary by canton -The proposed federal law has not yet been passed. Whether it will be enacted in the future, or what the final form will be, is anyone's guess.
Where are you moving to? For info on each canton's current regulations, see:
http://www.tierimrecht.org/de/tiersc...echt/index.php
In any case, I believe your Bostons should have no problems. It's the poor 'bull' terriers who have been (unfairly

) singled out.
One thing you should consider - have your dogs flown before? Some airlines have special conditions for flying the brachycephalic breeds - you'll want to look into that.
As for how easy it is to rent... kind of a roll of the dice.

As your dogs are small you are in an easier position than we were. Are you under much of a time constraint with the move?
With our mutts, temporary housing was not really viable, so I made a trip over to find the house first. The house I chose wasn't going to be ready for another 3 months, so the dogs and I stayed in the US for that time, husband moved into a short term serviced appartment, and we joined him in CH once we had the keys to the house.
When I was house hunting I was told housing would be a huge problem, but in hindsight I have come to believe that was simply the relocation agent trying to scare us and squeeze a higher rent/commission out of us. (So stay away from the evil corporate relocation people!

) Just stress to any potential landlord how well behaved and friendly and quiet your dogs are.
(You may have to pay a higher deposit - we did - but again, I think that was just our slimeball agent. Our Swiss neighbors, who had dogs and rented from the same landlord, did not have to put down more than the usual deposit.)
We settled for an old home in a town outside the city, with a large private garden. The house was small, nothing special, rather run-down, and far too expensive for what it was. But it had adequate secure space for the dogs to run and play, located in a dog-friendly neighborhood, with lots of great walks in the area - which was all I really cared about.
Make sure you have express permission to keep all four of your dogs written into the lease - this is very important. And, if there is anything else you need to arrange with the landlord - fencing, etc., make sure you have an agreement in writing.
You will want to consider taking out insurance against any damage the dogs might do to the rental property - as we found out to our cost, this was NOT included in the standard
Privathaftpflict (private liability) insurance package offered by Winterthur. We should have taken out a separate damage policy for that. So make sure your insurer understands your needs.
(And, stay away from the awful Swiss parquet flooring if you can! Doesn't stand up to the pitter-patter of canine feet, and is very expensive to replace if your landlord insists on it.)
Good luck with your move.