I've never used the Minibow, but I have 2 corner 5 gallon Eclipse tanks. Simply put - I love them. They have the bio-wheel (which is great), and they are quiet. I've never had an issue with them. I think the Minibow is a little cheaper than the Eclipse - but if you are lucky you can find the Eclipse on sale at Petsmart every so often.
I haven't used either, but both have been recommended on here by many people. Both seem to be the popular choice for Betta tanks!
As far as price range, I think the Minbows are cheaper. Someone posted on here about finding a 2.5 gallon on Amazon for $22 free shipping!
I have both my boys in a mini bow 2.5g desktop and they seem to love it, Jasper's the oldest so he knows more about it..but he seems to love it, having his own space and all.
As for me I love the smallness of the tank and the fact that it's big enough for the filter it come's with and a 25w heater.
I'd recommend it too anyone that's looking for a small / quiet tank.
The big difference is this: Eclipse filtration is awesome. Almost too awesome for bettas. The mini-bow comes with a gentler filter. Also, eclipses (except for the explorer) come with a fluorescent light, wheras I believe the mini-bow comes with an incandescent.
I have both now and If you can afford it I would go with the eclipse. The filter system is great and its quiet. Plus if your betta cant stand the flow its easily buffered.
The minibow (at least the one I just bought) Doesn't come with a heater. The filter for it takes up a lot of room although it is very gentle. The light is incandescent and doesn't put much light out at all. I'm trying to find a fluorescent that will go into it instead.
The only draw back to the eclipse is its hard to feed through as the door is made to open up to the filter. Most people have to lift the hood to feed.