I want to encrypt a binary file. My goal is that to prevent anyone to read the file who doesn't have the password.
Which is the better solution, AES or Blowfish with the same key length? We can assume that the attacker has great resources (softwares, knowledge, money) for cracking the file.
Probably AES. Blowfish was the direct predecessor to Twofish. Twofish was Bruce Schneier's entry into the competition that produced AES. It was judged as inferior to an entry named Rijndael, which was what became AES.
Interesting aside: at one point in the competition, all the entrants were asked to give their opinion of how the ciphers ranked. It's probably no surprise that each team picked its own entry as the best -- but every other team picked Rijndael as the second best.
That said, there are some basic differences in the basic goals of Blowfish vs. AES that can (arguably) favor Blowfish in terms of absolute security. In particular, Blowfish attempts to make a brute-force (key-exhaustion) attack difficult by making the initial key setup a fairly slow operation. For a normal user, this is of little consequence (it's still less than a millisecond) but if you're trying out millions of keys per second to break it, the difference is quite substantial.
In the end, I don't see that as a major advantage, however. I'd generally recommend AES. My next choices would probably be Serpent, MARS and Twofish in that order. Blowfish would come somewhere after those (though there are a couple of others that I'd probably recommend ahead of Blowfish).
It is a not-often-acknowledged fact that the block size of a block cipher is also an important security consideration (though nowhere near as important as the key size).
Blowfish (and most other block ciphers of the same era, like 3DES and IDEA) have a 64 bit block size, which is considered insufficient for the large file sizes which are common these days (the larger the file, and the smaller the block size, the higher the probability of a repeated block in the ciphertext - and such repeated blocks are extremely useful in cryptanalysis).
AES, on the other hand, has a 128 bit block size. This consideration alone is justification to use AES instead of Blowfish.
In terms of the algorithms themselves I would go with AES, for the simple reason is that it's been accepted by NIST and will be peer reviewed and cryptanalyzed for years. However I would suggest that in practical applications, unless you're storing some file that the government wants to keep secret (in which case the NSA would probably supply you with a better algorithm than both AES and Blowfish), using either of these algorithms won't make too much of a difference. All the security should be in the key, and both of these algorithms are resistant to brute force attacks. Blowfish has only shown to be weak on implementations that don't make use of the full 16 rounds. And while AES is newer, that fact should make you lean more towards BlowFish (if you were only taking age into consideration). Think of it this way, BlowFish has been around since the 90's and nobody (that we know of) has broken it yet....
Here is what I would pose to you... instead of looking at these two algorithms and trying to choose between the algorithm, why don't you look at your key generation scheme. A potential attacker who wants to decrypt your file is not going to sit there and come up with a theoretical set of keys that can be used and then do a brute force attack that can take months. Instead he is going to exploit something else, such as attacking your server hardware, reverse engineering your assembly to see the key, trying to find some config file that has the key in it, or maybe blackmailing your friend to copy a file from your computer. Those are going to be where you are most vulnerable, not the algorithm.
AES.
(I also am assuming you mean twofish not the much older and weaker blowfish)
Both (AES & twofish) are good algorithms. However even if they were equal or twofish was slightly ahead on technical merit I would STILL chose AES.
Why? Publicity. AES is THE standard for government encryption and thus millions of other entities also use it. A talented cryptanalyst simply gets more "bang for the buck" finding a flaw in AES then it does for the much less know and used twofish.
Obscurity provides no protection in encryption. More bodies looking, studying, probing, attacking an algorithm is always better. You want the most "vetted" algorithm possible and right now that is AES. If an algorithm isn't subject to intense and continual scrutiny you should place a lower confidence of it's strength. Sure twofish hasn't been compromised. Is that because of the strength of the cipher or simply because not enough people have taken a close look ..... YET
The algorithm choice probably doesn't matter that much. I'd use AES since it's been better researched. What's much more important is choosing the right operation mode and key derivation function.
You might want to take a look at the TrueCrypt format specification for inspiration if you want fast random access. If you don't need random access than XTS isn't the optimal mode, since it has weaknesses other modes don't. And you might want to add some kind of integrity check(or message authentication code) too.
I know this answer violates the terms of your question, but I think the correct answer to your intent is simply this: use whichever algorithm allows you the longest key length, then make sure you choose a really good key. Minor differences in the performance of most well regarded algorithms (cryptographically and chronologically) are overwhelmed by a few extra bits of a key.
Both algorithms (AES and twofish) are considered very secure. This has been widely covered in other answers.
However, since AES is much widely used now in 2016, it has been specifically hardware-accelerated in several platforms such as ARM and x86. While not significantly faster than twofish before hardware acceleration, AES is now much faster thanks to the dedicated CPU instructions.
