I've played this a lot since I got it and I would highly recommend it to anyone wanting to play jigsaws on the 360.
It only has a few flaws. You can't select a lot of pieces at once, to move them. You have to grab and move each piece one at a time. That's fine if your puzzle has less that 400 pieces. Around 800 it's tedious and over 1000 you're spending more time moving pieces than working on the puzzle itself. There is a way to throw pieces in a tray-type area then switch to the tray to pull them back but that process takes more work than moving the piece wherever you want it on the board.
You can't load images from a memory card so you're limited to the set of 30-something it comes. You can buy a space themed dlc for another 20 or so images. It's not bad.
Everything else about the game is great. It has a lot of options, modes (Classic on the highest difficulty is like putting a real puzzle together, the lower settings offer assistance and even hints if you hold a piece for 20-30 seconds), it has challenges, the controls are fluid and easy to use, and it would be good for beginners as well as advanced players. It's the best I've found on the xbox 360.
I've tried: Extreme Jigsaw Madness Jigsaw Guru Jigsaw Jumble Jigsaw World Picture Puzzle None of these are anywhere near as good as Puzzle Arcade.
If you prefer the PC you should try Jigs@w Puzzle Platinum Edition. It's the best puzzle interface I've seen. You can get it at: http://www.freedownloadscenter.com/Games/Puzzles/Jigs_w_Puzzle_Platinum_Edition.html