Joseph, 

Looks have a lot to do with your putter. However, yes, the various kinds of necks do make a difference/are built for a certain stroke. Putters with a "plumbers neck" (Newport 2) tend to be more for the golfer with an arc stroke. Same goes for the "flare" (Newport 1.5) style stroke, except they're more built for a golfer with a strong arc. 

If it's possible, get a hold of your local Titleist rep to schedule a putter fitting. It'll be well worth your time.

I think it is mainly personal preference but I think that the 1.5 inspires a little more confidence. It has no offset and is good for the 8-15 handicapper in my opinion.

The Newport 1.5 has 3/4 shaft offset and is for players with a strong arc stroke.  This is best if you typically pull putts.  The Newport 2 has a full shaft of offset and is great for putters who would typically push putts to the right (assuming you putt right handed).  It;s all about being able to square the clubface up at impact.  Also the 1.5 has a "flare/santa fe" style neck whereas the newport 2 has a plumber's neck.  Lastly, the 1.5 has the softer rounded shoulders of the Newport style head and the Newport 2 has the more square lines.  The best thing would be to try them both and just see what fits your eye and what you make putts with.  I don't want to sway you but I love the look of the Newport 1.5 and have already ordered mine.  It'll make a great backup to my 1.5 009.