I think that if you plan on staying for a long time, meaning forever, it is definately easier for Japanese.
First, Japanese people do not have to worry about visas. They are citizens and therefore are entitled to live here forever. Even if a foreigner has an easy time obtaining his or her visa, it is an inconvenience that a Japanese national will never have to worry about in Japan.
Second, there is the language issue. This may be true anywhere, but if you are illiterate, you will find yourself in big trouble soon. Learning to read and write Japanese takes quite a bit of time, even for Japanese people, but they have the benefit of learning it as a child on the same level with other Japanese people of the same age.
So very little that really matters is written in any language other than Japanese. Contracts, manuals, receipts, application forms, maps, etc. Not being proficient in Japanese and trying to do anything of substance (moving, buying a house or car, etc.) must be like pulling teeth.
How about the little things? You're lost in some place and you need to ask for directions. If you don't speak Japanese, good luck.
How about bigger things? You get in a traffic accident and need to call the insurance company and police. Don't know Japanese? Good luck.
Having relatives is important for obtaining contracts. This depends a lot on the company you're dealing with, but if you're renting an apartment on your own (e.g., not through your company), having a relative co-sign your lease makes things go through a heck of a lot easier. Some places won't accept co-signers who are not relatives except under special circumstances, and then they still don't carry the same weight.
Making friends is much easier if you speak Japanese, unless you're content with having mostly foreign friends. Foreign people have a bad tendency to move out of the country, though.
However, I do agree with Caster in a sense. If you're here short term for the JET Programme and in your 20's, you probably have it easier than a similar Japanese person of your age. However, depending on where you're sent, it might be hell, too. I have heard of a JET who was placed in the middle of nowhere, and she was literally bawling and pleading to go home after only being there for one day!
Having said that, after spending some time on Gaijin Pot, I understand how people can have an easy time in Japan as a foreigner. But those people are only here on short term and mostly seem to want to play around, anyway. Those people I don't include in my 'analysis' above.