I use Corps of Siege infantry for offensive operations, as mentioned above it's nice when a single unit (regiment) can force retreats as you approach the objective, and a siege rgt has enough artillery to be useful in indirect attacks to prep a target while other units get into place. I still used multiple MG Inf Brigades to guard flanks/road network, or deal with rebels, when I want to cover a lot of hexes or be able to easily surround a unit. In my last game, I had saved up the IP and metal/rares for a Mech Assault Corps, until I got to the second screen and saw the fuel cost, which would have exhausted my entire stockpile! So I used brigades (one armor, one mech) on each front which worked out well for encircling units.
As for advantages, two that haven't been mentioned are leaders and posture strategems. I don't worry too much about using a Junior on an MG Brigade, but for my lead assault forces, I want the best leader and the ability to use an effective posture (Infiltration works well for the Siege corps). If I had an equivalent # of brigades, I don't think I'd have enough posture stragems for all of them, and definitely couldnt count on using Mercs with high combat skills for each bde.
Early on, I found it easier to build siege brigades, and then upgrade them to corps as I had the resources, that way the leader and sub-units can gain some XP, then you fill them out to make the larger attack force. It's especially useful when preparing for a war, you can raise the brigades at a city, then position the brigades on the front line, upgrade them as you invade and within a couple turns (as long as you buy all the replacements) they build their strength as they get closer to the enemy cities.
Playing/Learning Shadow Empire