My brother went to Lawrenceville, and my son is now at Hotchkiss. Both great schools. I know nothing about Peddie.
If there are any differences of note between Hotchkiss and Lawrenceville, they are, IMHO, as follows: (a) THS offers more classes per student than L'ville; (b) the endowment per student is greater at Hotchkiss than at L'ville; and (c) the list of renown THS alums seems a little more impressive and deeper than the Lawrenceville list. That said, you can't make a wrong choice if you are deciding between Lawrenceville and Hotchkiss. Deem yourself most fortunate.