The 6100 is 8.08mm, the 1815 is 8.8mm. Good comparisons, sub seconds dials, similar diameter with the Lange being slightly smaller. Same price point.
Other quick comparisons may be:
Annual Calendars : 5205 is 11.36mm. 1815 Annual Calendar is 10.1mm. One is automatic, one manual so the difference can be accounted for somewhat.
Chronographs : 5172 is 11.45mm. 1815 Chronograph is 11mm. Do people recognize that the Patek is a thicker watch?