Different monsters will be different in different ways, too. A earth elemental is CR 5 in both systems, but the 3.5 earth elemental is a CR 6 when counted using 5e's guidelines. Other monsters can be different. The 3.5 ghast is a CR 3, but its calculated stats put it as CR 2 in 5e's guidelines. Then you get to the high level enemies. A mature adult black dragon in 3.5 and an adult black dragon in 5e are both CR 14, but the 3.5 version has +28 to attack, an AC of 29, and a frightful presence DC of 23. A DM could still use this stat block, but these stats would have to be recalculated under the 5e system.
So lower CR creatures can be "close enough", but in general the monsters, especially those of higher CR, will need to be checked and modified to fit 5e's bounded accuracy range.