Ultra has Modern 'D' NECK it is shallow in sense your thumb is closer to fretboard and allows you to stretch fingers easier on fretboard; it is far from chunky and yes should give it a play. I find it extremely comfortable, fast and easy to play; also neck width is only 1.625 so good for even small hands.
I thought 1.5/38mm necks were for Guitar Players who were sentenced to playing bass by bandmates😀
quote from review
'With Fender’s new “Modern D” neck shape, which is a slimmer neck with ultra rolled edges, a 10”-14” compound radius, and a tapered neck heel that allows easy access to the higher frets, the American Ultra Precision Bass is a hell of a lot easier to practice or gig with. It was comfortable to play for hours without getting tired because of the delicately contoured backside—it seemed to hug my body.''