Flown with them both, and in fact am flying with both later this year. They are of an equal standard IMO. Cabin baggage?..pot luck with both,just make sure you get to the gate early. Most Monarch have been refitted with the new seats which are an improvement on the older types,although others may disagree, but maybe not so good after 5 hours on either carrier.
As for service, generally very good on both, but as always its a people thing and therefore depends on the crew on that flight. Personally I always find crews on both companies to be pleasant and helpful. Easyjet wise I always fly out of Liverpool and they have some real characters out of there