Space Invaders is one of my favorite games. Still trying to get a nice one. But I would still probably have to go with Gorf if I could only own one. I love Gorf - the gameplay is great, and I love that speech feature. Space Invaders definitely has a cooler cabinet though, and it's also an awesome game. But... Space Invaders is also a lot more common than Gorf... but it seems to be a lot harder to find one in good shape. Space Invaders also has a lot more "classic" to it. Everyone recognises Space Invaders. Not so much with Gorf.
I love the Space Invaders cabinet design though. With the mirror, backdrop, and black light, it all fits together perfectly. You don't feel as much like you're looking into a monitor, you just see the image. I love the fact that they combined simple, clever tricks to make the game seem even more impressive (colored strips on a black and white monitor, printed cardboard background graphics, etc). Space Invaders also has that awesome low thumping noise like Asteroids. The game has a "presence" all it's own.
But, it looks like Gorf is also going to be cheaper - I'm sure you have spare monitors laying around you could put in there.
Edit: If you do intend to buy Gorf - make sure it works, and the speech works (that speech chip is hard to get!). That boardset is kinda complicated. You're going to probably want to make sure you can test the video output - because the pattern transfer board can be bad, and the game will still play fine - just with bad graphics. And that board is a pain to repair. If there's a bunch of horizontal lines in the picture, it's just a bad RAM chip. Usually, your ship will explode when it touches one of those lines (i.e. instantly).
-Ian