Read Snatch Steal vs Cyber Phoenix. Snatch Steal is SLIGHTLY different then Brain Control/Enemy Controller cause of, yes, since it's an Equip Spell Card.
What happens when Cyber Phoenix is on your field, and you use Snatch Steal to take your foe's Cyber Dragon.
#1: Snatch Steal effect kicks in, and Cyber Dragon goes to your side of the field.
#2: Cyber Phoenix effect kicks in, negates Snatch Steal since it's targetting a Machine monster (i.e. Cyber Dragon) and goes back to foe's side of the field.
#3: Now it's back to foe's field, and now Cyber Phoenix effect is no longer in effect, (Because since the Cyber Dragon is back to the foe's field, Snatch Steal isn't targeting any machine monster on your side of the field) so Snatch Steal effect kicks in, and bring back Cyber Dragon back to your field...
#4: Again, now Cyber Phoenix effect kicks in and... you get the picture.
So, it's an endless loop.. So this is ruled as illegal play, and the player who activated Snatch Steal have to take it back.
Yes, Snatch Steal is different then Enemy Controller/Creature Swap/Brain Control/etc. cause it's an Equip Spell card and Cyber Phoenix will negate all Equip spell card effects equipped to machines.
The thing about Enemy Controller and Brain Control, once you activate it, it's DONE. The "on your side of the field till end phase" is the lingering effect of the resolution/effect of Enemy Controller and Brain Control. So by the time a Machine monster is stolen by Enemy Controller/Brain Control, it's already not being targetted by anything and thus Cyber Phoenix have no effect.
Premature Burial/CotH is slightly different too. When you activate it, it's targetting a monster in the graveyard (even if it's a machine) Cyber Phoenix negation effect is a FIELD EFFECT. And thus CotH/Preme resolves. Now, when it brings a machine monster on the field with Preme/CotH, now Cyber Phoenix effect kicks in cause it's targetting a machine monster. So the 2nd effect of being destroyed when Preme/CotH is destroyed/removed is negated. (This also works when you target Cyber Phoenix in grave with Preme/CotH as well)
I hope this helps.