I take it if you are going to move both filters that the old tank will no longer be used.??
In my opinion it will mean that there is no real cycling process as the filters will already be cycled. However, the tank will only be cycled for the equivalent bio-load to that of the old tank. If you are adding new fish, you still want to do this slowly. Although, if the tank is previously pretty well stocked and the filter is pretty mature, the filter should be able to allow the growth of the additional bacteria pretty well as you add fish. You may not even notice a mini-cycle.
I used to just have an internal Juwel filter, but after a few months i added and external eheim filter, with the aim of removing the juwel one to create more space. I ran the two along side each other for about 4 weeks (perhaps longer than i needed to, but wanted to be sure) then removed the juwel filter. I continually tested the water, and the stats showed no ill effects/signs of ammonia or nitrite.
Hope that helps,
Squid.