De arimasu and arimasu are quite different. De arimasu is 1/2 of desu, the other half being de imasu.
Desu is a contraction used to simplify things. Technically 'watashi wa Hayashi desu' would probably be 'watashi wa Hayashi de imasu', and 'sore wa MechWarrior desu' is 'sore wa MechWarrior de arimasu'.
But the de arimasu and de imasu forms are horribly antiquated. It probably used to be the case that changing form to honorific form would change all de arimasu to de gozaimasu and all de imasu to de irasshaimasu, but as of now de gozaimasu has become formal form while de irasshaimasu has become honorific form, irrespective of whether you're referring to an item or a person, because the de arimasu and de imasu forms they came from were collapsed into a single desu, making the original distinction irrelevant.
It's kind of hard (read: probably impossible) to learn Japanese from an online forum like this. 2 years of formal instruction from native speaker instructors and spending time with native speaker friends later, my Japanese is still nowhere near what a native's proficiency would be. If you're interested to learn I would really advocate finding a language school near you.
Where I study, Japanese is the #1 hardest foreign language (Mandarin Chinese is the #1 hardest language, but it's not considered foreign) that is offered by the university. It has the largest enrollment rate, accounting for 50% of the language school enrollment at level 1, but because of its difficulty has the highest dropout rate, reducing to 20% of the overall enrollment by level 6. The main difficulty is the grammar - which online translation sites are incapable of replicating, resulting in debacles like 'all your base are belong to us'.
There are theoretical grammar considerations and usage grammar considerations as well - and between the two, what is used commonly will be considered as more correct even if it flies in the face of theory. A good example would be denwa - as it is a Mandarin-direct translated word, denwa should be prefaced by go, making it ご電話, but in practice, it is prefaced by o instead of go, for unknown historical reasons.
As such, unless you have a good reason for doing so, deferring to the native speaker while learning is more likely to be correct than not, and learning to accept that what you thought was correct is actually wrong/has exceptions is more or less an everyday thing when you start learning, particularly at higher levels. Humility has a large part in Japanese culture, and you can't learn the language properly without picking up some of the culture as well.
Using one without the other would REALLY annoy the native speakers for one thing.
Edited by Hayashi, 26 November 2012 - 12:20 PM.