It depends. There are nuances depending on the implemented standards. If they are operating on similar standards, it is possible for a user to move their credentials to another wallet.
Mobile Wallet : When dealing with a strictly edge wallet on a mobile device, their will always be size and ease of use complexities (large, no backup, no multi-device synch across web and mobile apps).
Cloud Wallet : Easier to implement, recoverability, multi-device, etc. Not as secure.
Trinsic’s Hybrid Wallet : Best of both worlds. Only the private key is stored on the edge (small size, wallet is encrypted in the cloud and only accessible via the user’s private key), while information can be shared (multi-device) and recovered on the cloud.