I don't have these, but I do have ON1's Perfect Resize, which does a good job of enlarging small or crappy images to 'better' levels,. though it would not improve a truly awful image. Adobe Photoshop (current version) is pushing their 'neural filters', a couple of which do a decent job of enlarging and improving images, especially removing JPEG artefacts. Some reviews of the Topaz products have said that they work well on some images, but not all, and most agree that it's an expensive experiment.
Of course, starting off with the best quality will reduce the need to piss about afterwards! I use the phone for snaps or exploration, but still use the SLR and flash for quality shots, especially if they might be published.