I see lots of Xbow broadheads advertised along side vertical bow broadheads

Are they the same, except for the packaging?

I use the same heads for all. The only time i have ever had a problem was if a head was bent, so it did not fly true.
The only type of broadhead i would avoid is the fixed two blade with small crosscut bleeder. I had an issue with them planing off target.

Generally - and this a broad statement, the mechanical broadheads for crossbows have some type of extra tension on the blades in the closed position to keep them from "popping" open on the shot.

Most crossbows are pushing the bolts somewhat faster than the same weight in a vertical bow, so any issues with the flight of the bolt are going to be that much more obvious.

My arrows are around 400-415 grains, and my bolts are 420-425 grains. The vertical bow pushes the arrows at 285-ish, and the crossbow is driving the bolt at 320-330. If the head isn't flying well from the vertical bow, it's probably not going to improve with the extra speed on the bolt.

I've had the same issues as noted above with the broad single blades and bleeder vanes, they were either dead-on, or continuously planing away.

Because of the typical speed and mass advantages of the crossbow arrows they can do a better job with big cut mechanicals, but the advantage is not huge.

There's no tuning with most xbows, so throw in the extreme speed and you can get really wild flight with many fixed blades. The way I've found to overcome this to some extent is by using arrows with really high FOC weight and heads with small CD. Or you can just use a mechanical.

+1 on the comment of Xbows causing some mechanicals to snap open in flight. Always best to go with heads that can take that force. I do use some normal type expandables with O-rings or rubber bands and just double up to keep them closed.