Well I think you have learned an important lesson here. And that is, when you get a new [different] cue, it plays differently. And depending on the differences and how long you were playing with your old cue, it may take a few months to a year or two to re-learn how to play with your new cue.
The things which can change are...
-Weight of cue and this can goof up speed control - accurately shooting with an exact speed. And many cues are not the weight you may think they are. To find the REAL weight of cues, you need an accurate scale. I would recommend 19.5 oz for a playing cue. Weights can be adjusted in better cues with weight bolts. Be sure your cue maker is using an accurate scale as well.
Get accurate scale here...
(I got the KD200-110 which is more accurate with lesser weights)
http://www.scalesgalore.com/tanitakd200.htm
-Taper - pro or euro taper. Custom cues can have *any* taper you desire. A different taper will "feel different". Can take awhile to adjust to.
-Shaft diameter at tip. 11mm, 12mm, 13mm, etc. Can't use a dime shaped tip if diameter too large since edges of tip curve will go down to ferrule. A different diameter will "feel different". Can take awhile to adjust to.
-Tip. A new cue might have a different brand/type of tip, hardness of tip, and shape of tip (nickel, dime, quarter). This can change cue ball deflection with english shots - thus aiming might be off when using english.
-Deflection of shaft. Different cues have a different mass near the tip. This will make the cue ball deflect differently when using english.
My experience with switching to an entirely new cue is problems with aiming when using english mostly and then speed control if switching weight.
The thing to do NOW is find out what brand/hardness of tip you have on your new cue. And what shape it is (nickel, dime, quarter). Then when you need a new tip in the future, you can get the same thing and shape it to the same radius. If you keep it shaped to the same radius always, then when replacing the tip, the new tip will play the same as the old.