How much is more significant? Sent Via Telekinesis
Side by side, the Majestic is probably twice as thick. I want to say the Majestic stripe is closest to a full 1cm, while the Honigs stripe is about 0.5 cm. Now as far as appearance goes, from afar in the stands or so, you can't really tell the difference. They still come out to look the same, just the Majestic has a thicker, brighter white stripe.
(On a side note, I would say the OC mlb style shirt is right in between the two in the stripe widths, in case that gives a better example.)