The Shield really is a wonderful gaming device. It does what it's supposed to be doing really well, that is providing the best tablet gaming experience available there is. The 720p screen something most people aren't crazy about, but it still looks surprinsingly sharp.
That being said there was one issue with this... and it's that while the Shield plays Android games like no other tablets, there aren't that many Android games available that will make you happy you spent 250-300 bucks on a Shield. Not to mention that some Android ports actually have toned down difficulty to make up for the natively horrible controls, making playing these games with the Shield feeling rather boring.
Where the Shield truly shines is when streaming games from your PC GeForce card. If you don't own one (note that you need a card from this year, and a very good and expensive one), you're missing out on the best thing it has to offer, and suddenly the offer becomes a lot less attractive. It's still a good device, and if you're really more serious than I am with your Android gaming, this is the ultimate device right now on the market. It's only gonna lose that recommendation when the Shield 2 comes out...
The iPad on the other hand has a richer games offering, but you're going back to that dreaded tablet format and controls which only works well for very casual gaming. Still, definitely a richer library.
Performance shouldn't be affecting your decision too much as they're both powerful devices that few (read none) games will utilize to their full potential. Still, the Shield is likely to outperform the iPad most of the time... but has a lower resolution.
Always pros and cons
Using these last lines to throw objectvity out of the window, I would say that if you only wanna use your tablet for gaming, you definitely wanna go with the Shield. It's cheaper than the iPad, will provide a much, much more enjoyable gaming experience and you can still absolutely listen to movies and music on it, as well as downloading any other apps you please. And if the 720p screen is a turn off for you, news of a Shield 2 in the work coming out "sooner than you might think" are growing louder and louder. So my personal opinion would be to either buy a Shield, or wait for a Shield 2. Never liked Apple and their overpriced products anyway