Is a Boss DD-3 going to work with bass? What do you guys think of it?

Do think it's worth spending an extra 50 bucks and getting a Boss DD-7?

Are there other Delay pedals I should take a look at for like $150-ish?
Yep works fine. Dont think its worth the extra $$ for a few extra options.
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My Axe: WarwickThumb
I just got the DD-3, its pretty neat. I'm glad I didn't spend more. For $150 you can get the Carbon Copy which is an analog delay. The DD-3 is digital.
DigiTech: DigiDelay X-Series Digital Delay. I believe (don't quote me though) that Fitz recommended this one to me. I love mine; its a great delay pedal for both guitar and bass.
I have the dd6, which cost as much as the dd7 before the 7 came out, and I'm glad I have the extra delay modes and greater overall delay time. The seven seems even better with everyone praising it's analog emulation setting can create simple loops on it, and can use an expression pedal with it to controll some parameters. I say save for the seven if you want more to play with, but don't bother if you know the dd3 already has all the options you'll need.
..they work great with bass, they suck tone a bit if they're in front of an amp instead of in the effects loop though.
What the difference between the Analog and the Digital soundwise? I'm kinda looking for something to get an Angels & Airwaves-type sound.
It's hard to explain, and honestly a lot of people can't tell a difference most of the time. Think of digital as slightly more articulate, but also cold or even sterile
Think of analog as more organic and "natural" sounding, but often with slightly less definition (I don't really mean this as "muddy" or anything like that... words fail me).

A digital delay will be much more versitile and provide much longer delay times than an analog. An analog delay, however, provides a timbre that some musicians specifically want.

Think of analog signals as sin waves, and digital signals as staircases going up and down, one is a natural curve, one is a series of steps that approximates the sound of a natural curve when the human mind averages the steps out. I can't really explain how that actually translates into sound any better than I have done above.