Ibanez AEB10 or AEB45.
I have played a lot of A/E basses, plugging them in, unplugged. Of them all, the Ibanez's sound best plugged in and near the top unplugged. Even once getting into the higher end of cost, plugged in the Ibanez's continue to sound the best. They are also set up well and easy to play. I like the AEB10 for the slightly smaller body. You lose some volume, but you don't miss it plugged in.
If the Ibanez's aren't to your taste, the Michael Kelly's aren't bad. The Fender AE basses sound OK unplugged, but awful plugged in (to my ears, your mileage may vary).
Once you go up in price, there's a SWEEEEEEEET one made by Blue Ridge. Holy schmoly. Made my jaw drop. There was nothing I didn't like about it but the price. Were I to have the money, this one would be mine and the Ibanez (though a terrific value) would be forgotten.
Breedlove makes a dandy AE bass as well. Also pricier than the Michael Kelly or the Ibanez. Very nice. Good sound and projection unplugged, perhaps the best of this lot. No AE bass is going to project as well unplugged as a guitar. I don't know why that is, but it seems to be the case.
I played the Takemine one, but it definitely felt like a bass made for a guitar player to me. I'm a bass player at heart, so I want a big full neck and heavy strings. It feels 'right'. The Takemine sounded OK, and it would be easy for a guitar player to play because the fret distances and set up felt more guitar-like than bass like to me. I didn't plug it in, so can't comment on the plugged in sound.
Guild made a dandy one for a while, but it was expensive and I didn't feel that it sounded any better than the Ibanez AEC10 that costs about 1/3 the price. The AEB10 is definitely the best value I've seen out there, followed closely by Michael Kelly. The nice thing about Michael Kelly is that they make a fretless 4-string and a fretless 5-string (if you're into having a 25% string overload on your basses). Having started bass playing upright bass in a classical orchestra, I like fretless. There's good reasons to go with a fretted model, especially if you're playing mostly country or rock, though.
My indistinct ramblings, hopefully helpful.
- Zurf