Encryption functions (block ciphers) cannot take in an arbitrary lengthed input. So even if you encrypt the entire file, the encryption function itself is going to break it into blocks and encrypt the blocks individually. This is similar to encrypting individual records, except that the mode of operation will dictate if/how these blocks are mixed with each other.
By encrypting each record individually, you are doing something akin to the ECB mode of operation. The difference is that you have partitioned the data yourself. This preserves information about the structure and any attack against ECB will also apply to the approach of encrypting records individually (without random padding). For example, if two records are the same, you will be able to see that in the ciphertext.
Also by encrypting each record individually, you are not filling the blocks up completely which will be less efficient in terms of speed and storage.
So the short answer is: it is much better to encrypt the whole file and to use a good mode of operation to do it (CBC or XTS for example).
The only reason you would consider not encrypting the whole file is if you need to selectively decrypt records efficiently or replace records. Encrypting the whole file means to fetch a record, you need to decrypt the whole file up to the record you are interested in. And changing any part of an individual record means reencrypting the rest of the data. If this is a concern, there are standard ways to do sector-by-sector encryption.