I emailed Pat Reilly and he was kind enough to reply:
"The is a lot of tradition associated with the use of clips. As you mentioned, is is common in Europe for horses to be shod with toe clips on front feet and side clips on hind feet. This is likely because hind feet twist as they land and the side clips provide additional stability to this rotational force. Front feet do not twist when landing (as a general rule), but front shoes sometimes slide back on a hoof. Toe clips (and side clips, if the clips are in front of the widest part of the hoof) will prevent the shoe from sliding back.
There are several reasons side clips on front feet have become common in the US. Many farrier chose to set the shoe back on the hoof (easing breakover), and this is more easily accomplished without a toe clip. Some people oppose the use of side clips for fear of contracting the hoof, although science has shown that clips do not interfere with hoof expansion.
If your horse is sound then you are probably fine continuing as your farrier would like. The mechanical difference between side and toe clips is very small (if there is any difference). I think people tend to notice the clips because they are the most visible part of the shoe, but if the shoe is not falling off then you probably don’t have much to worry about. Farriers often have a personal preference, and I would recommend that you allow them to shoe the horse as they would like as long as things are going well. "