I am saving my ass off to buy something special. I am a lefty so the range is fairly limited and its difficult to walk into a store and try too many guitars.

1 guitar available in lefty that I love the look of is the EB Music Man JP BFR 6. No stores around me stock them so i haven't had the chance to even pick up a right hander so i can look at it closely.

Theres enough specs available online to know that its an unbelievable guitar, but i can't seem to find full neck dimensions in terms of thickness. Can anyone tell me how the neck stacks up comaratively to something like the Ibanez Wizard necks.

From memory: it's a bit thicker than a Wizard neck and the profile is a bit rounder (Wizard necks aren't just thin, they're pretty flat, too).

The neck on the BFR is incredible, though. In fact, the whole guitar is great, definitely one of the best I've ever played.
You've read it, you can't un-read it!
from my experience with the JP7, it was a very flat and thin neck, very similar to ibanez but a bit more rounded.

That was just the one time i played a normal JP7, I also have limited experience with ibanez necks because i dont like either neck shape that much but hey it maybe your cup of tea, im personally into thicker necks
From the Music Man website on the Petrucci BFR:

John Petrucci BFR 6
The Ball family is the last of a dying breed, a family business making guitars and basses exclusively in the United States. Ball Family Reserve is a celebration of our heritage in instrument craftsmanship which features some of the finest figured tone woods and finishes available. These rare heritage pieces will be offered in limited runs and allow us to present instruments to the public that were previously reserved for family and our loyal artists.
12-3/8" wide, 1-3/4" thick, 37" long (31.4 cm wide, 4.5 cm thick, 94.0 cm long)
8 lbs, 7 oz (3.83 kg) - varies slightly
Body Wood:
Alder with bookmatched maple top and mahogany Tone Block. Honey Bursted Koa Top - Mahogany body
Body Finish:
High gloss polyester
Standard - Custom John Petrucci Music Man® Piezo floating tremolo of chrome plated, hardened steel with solid steel saddles. Koa top - Custom John Petrucci Piezo floating tremolo with gold plating
Scale Length:
25-1/2" (64.8 cm)
Neck Radius:
15" (38.1 cm)
Headstock Size:
Only 5-7/8" (14.9 cm) long
24 - High profile, wide
Neck Width:
1-11/16" (43.0 mm) at nut, 2-1/4" (57.2 mm) at last fret
Neck Wood:

Maple top - Rosewood; Koa top - Ebony
Fret Markers:
Custom JP Shields and Mother of Pearl BFR inlay at 12th fret
Neck Finish:
High gloss polyester
Neck Colors:
All black neck with black headstock; Tobacco Burst - Color matches body with matching painted headstock
Tuning Machines:
Schaller M6-IND locking with pearl buttons
Truss Rod:
Adjustable - no component or string removal
Neck Attachment:
5 bolts - perfect alignment with no shifting; Sculpted neck joint allows smooth access to higher frets
Electronic Shielding:
Graphite acrylic resin coated body cavity and aluminum lined control cover
500kohm volume, 500kohm push/pull tone for custom 2 pickup configurations - .022µF tone capacitor
3-way toggle pickup selector, with custom center position configuration; 3-way toggle piezo/magnetic selector
HH - Neck: DiMarzio LiquiFire, Bridge: DiMarzio Crunch Lab
Left Handed:
9p-11p-16p-26w-36w-46w (RPS Hybrid Slinkys #2241)
"Maybe this world is another planet's hell?" - Aldous Huxley
^Width =/= thickness.

The MusicMan necks are a little bit thicker and more rounded than a Wizard. Width wise they're basically the same, but because the neck is more rounded, it doesn't feel quite as wide (Thin flat Ibanez necks always feel wider to me)