I think they are all nice machines. I have the Babylock (BLQP). It is a 9" machine and almost identical to the Brother 1500. I would be happy with any of the 3 machines you mentioned.
Linda OH

I chose the Juki to run on my frame (different frame than yours, but same concept). I took it on a suggestion of a few members here, one with the same frame as me.

The thread cutter is almost a necessity for this purpose. The Juki runs fast, but can be tricky to learn tensions/thread types. (I'm still learning to use mine efficiently.)

Good luck with your choice.

treynmama,
I have a Janome 1600DBX DO NOT LIKE IT! it Sews horrible on the frame. Off the frame no problem! I have talked with several others that have the same problem. The needle is a pain to put in. it also only takes DB needles....the tension is horrible on the frame, You can not lower the feeddogs you get a plate to cover them.
It is also only a 9" throat!.My Janome does not have automatic needle threader and it is a pain!

If I had to choose between what you are asking about I would go with the Brother!

the brother
High speed straight stitch machine with max.1,500 stitches per minute

Expanded work area for large projects with more than 6" height and 9" width in the fabric bed area right of the needle

Heavy-duty construction for increased stability and penetrating power

Up to 7 mm stitch length for perfect stitch lengths or basting

Exclusive pin feed mechanism to prevent slippage

Knee lifter and optional bed extension table for quilting and fabric management of bulky projects

Built-in telescopic thread stand for cone thread usage

Full range feed pressure adjustment and 4 feed dog height settings for different fabric weights

Tension adjustment dial for different fabric and thread weights

Exclusive fabric separator feature joins lightweight linings to materials such as velvets and eliminates the puckering

Easy to use foot lift operation-the lower feed dog drops automatically when the presser foot is lifted for easy fabric insertion

Removable knee lift enables you to lift your presser foot leaving both hands free for fabric handling

The feed dog adjustment knob lowers the feed dogs below the fabric plate for free motion sewing (drop feed control)

Exclusive F.A.S.T. automatic needle threader saves time and your eyesight

Built-in automatic thread cutter activates with the touch of a button both top and bottom threads are neatly cut and threads are instantly reset for the next sewing operation

Needle positioning mechanism lets you control needle up after needle stops down

Eliminates the need to manually rotate the balance wheel to lower or raise the needle during a continuous stop and start sewing operation

150 watt motor, 1.5 amps, 2 to 3 times more power than most home portables

Optional 12" x 18" extension table is included on the Brother PQ-1500S model

Good luck in your search.
Red

Thank you all so much for the info, I think I have made up my mind. I have researched on the internet and read some really bad reviews on the Juki, one person said it should be called the "Junkie", and the review on the Janome wasn't too much better. So I think it is definitely the brother. Thanks again for the input, it is appreciated.
Treynmama

I see you've made your choice but I just wanted to add I love my Juki on the Hinterberg frame. I had trouble in the beginning but was it wasn't the machine it was the user. I would buy this set up again, of course I would love to have a 16" or 17" machine but that's out of my price range.

treynmama,
i have the brother and use it on a low end grace frame and love it. the only problems i had were user error, and time has fixed that. good luck and smooth quilting. only thing i would recomend is stich controller or handi handles ( my hubby made me a stitch controller for about 10$ worth of parts from radio shack)
donna