It's a great idea but I agree with one of the comments... it will eventually leak water or burst because the foam particles aren't fully sealed and water will be absorbed through them.
You can test this by placing water in a styrofoam cup and leaving it for a couple of days, you'll see drops of water coming thorugh (not condensation!)
I would combine both ideas into one. Get the cheapest and larges plastic tub, cut the opening on one side and attach the glass. You would get a tank with a lid and a clear side.
Ya eventually it would break. So good for your basic hopsital tank for only a couple weeks at most.
I like using plastic tubs for bettas in general, they also seem to like them. I'm gonna use a mixture of spawning methods: traditional hobbyist and shallow spawning. Shallow spawning is in the plastic tubs stuffed with live plants but I'm sure you read about it on www.bettysplendens.com
Anyway just some nice videos on making cheap tanks.
Who am I? Well I am a Junior Member of the International Betta Congress and a breeder of white HMPKs, red dragon HMPKs, black/red dragon HMPKs, metallic multi HMPKs, blue masked HMPKs, and now multi color HMs. Soon to add black HMs. I will be showing in New Breeder class in fall of 2012.