I almost always get some degree of change, typically down .5-1.5MOA. Sometimes a bit of a lateral shift. The lateral shift can sometimes be rectified by having the can indexed to the barrel like Elite Iron does. Their cans only have vertical changes, much easier to deal with.
In general, the lighter the barrel, heavier the can and the looser the can attaches will all aid in shift. Some can be accounted for, some not. I have my rifles with dedicated cans so I just record the difference and when a can goes on, I make the change and vice versa. Think about it: with barrel harmonics, wouldn't a lighter, thinner barrel along with a heavier, loose fitting can cause more whip?
Some of the shorter and heavier barrels with lighter cans (like my 8.5 Noveske .300BLK bbl. and Ultra 5 can) have almost zero noticeable change. My worst is an AAC SDN6 that uses a fairly loose mount along with a fairly long and thin barrel. Change can be 2MOA or more low.
My better cans, my indexed .50BMG Elite Iron has very little shift despite weight and size; it's also indexed and very well made. The Saker is similar too, very tiny vertical shift despite weight. Ultras do well in general, just so light and with tight fitting mounts. So do short cans. AAC is the worst but they wobble and wiggle a lot without work, but I got 'em cheap. Wish I'd just bought Sakers instead though.