RE: Minor league baseball vs minor league (AHL) hockey
As a few other people have noted, there are a few big differences between the minor leagues for the two sports. Most of these factors have already been noted, but this post is meant to identify all/most of them in one place.
1) Baseball is significantly more popular than hockey in the U.S.
2) Minor league baseball is significantly cheaper on a per game basis than minor league hockey, making it more family-friendly and financially-friendly to casual fans.
3) Minor league baseball is played in the summer time outside, which attracts families, groups, and casual fans looking for an outing that happens to be at a baseball game. By contrast, minor league hockey is played in the winter inside, which means fewer people treat the games as merely an outing.
4) Because minor league baseball is played during the summer when school is out of session for most kids, there are usually fewer schedule conflicts for most fans, especially fans with kids, than there are for minor league hockey.
5) Minor league baseball places greater emphasis on non-game related entertainment than minor league hockey, which attracts more casual or even non-fans.
6) Baseball is a more relaxed game to watch in most cases than hockey, which makes it easier for the casual fan to follow and understand (important factors when you're talking about the minor league versions of the two sports).
7) In most cases at least IMO, rivalries are more heated in hockey than baseball, and minor league baseball fans are more likely to root for a local team that has a parent club they dislike than minor league hockey fans are (though if fans truly hate a parent team, they aren't overly likely to root for the local minor league team in either sport).
If the above factors could be generally summed up, it would be that it is easier for minor league baseball to attract casual fans than it is for minor league hockey, and that due to the nature of the two games style and schedule-wise, it is more likely baseball fans will follow a MiLB team not affiliated with their favorite MLB team than hockey fans will follow an AHL team not affiliated with their favorite NHL team.
Speaking as someone who has attended literally hundreds of minor league baseball games and at one time lived in a minor league baseball city and would attend about 20 games per year for that team, I can tell you that I personally would have no problem rooting for a minor league baseball team not affiliated with my MLB team and actually root for my local minor league team against an affiliate of my MLB team. (In fact, I actually did that when I lived in the aforementioned minor league baseball city, Harrisburg, and they would play Reading, affiliated with my MLB team, the Phillies. More specifically, I'd root for Harrisburg to beat Reading and for the Phillies' prospects in Reading to do well.) By contrast, I still have had some trouble warming up to the Lehigh Valley Phantoms (located in the area where I grew up) when I've seen them play during family visits. I can't say this for sure, but if I had the opportunity to attend an Albany/Lehigh Valley game (or in future seasons, a Binghamton/Lehigh Valley game) in Allentown, I'd probably root for the Devils affiliate over my home region team (or perhaps wear mixed apparel, like a Devils jersey and LV Phantoms hat).