What OFX is
OFX is the format behind the Download Transactions button on your bank's website. Version 1 is SGML, where a leaf element has an opening tag and no closing one. Version 2 is real XML. QFX is Intuit's variant of the same thing with a few extra tags, which is why a .qfx file opens in Quicken and is refused by software that only knows plain OFX.
Retail banks, credit card issuers and brokerages, because it is what Quicken and Microsoft Money asked for and the industry standardised on.
What TSV is
TSV is CSV with tabs instead of commas. Because tabs almost never appear inside a value, quoting is rarely needed and the files are easier to read by eye.
Bioinformatics, log processing, and anyone who has copied a block of cells out of a spreadsheet: the clipboard format is TSV.
What changes when you convert OFX to TSV
Each STMTTRN block becomes a row: date, amount, type, payee, memo, cheque number and the bank's own transaction id. The account number and currency come from the statement header and are added to every row, so a file merged with another still says which account it came from. Both the SGML and the XML flavour are read the same way.
Pick TSV over CSV when your values contain commas. Pasting the result straight into a spreadsheet fills the cells correctly with no import dialog.
What carries over from OFX to TSV
OFX records 3 things about a table that TSV has no way to hold.
OFX distinguishes a number from the text of a number; TSV does not, so every value arrives as text and has to be re-parsed by whatever reads it next.
An empty cell and a missing one are the same thing in TSV, so a null and an empty string in the OFX both come out blank and can no longer be told apart.
OFX can hold a value that is itself a list or an object. TSV has only flat cells, so nested values are flattened into one cell rather than being spread across columns.
The result can be read a record at a time, and appended to by adding to the end of it. That is worth having for a table too large to hold in memory, and it means a TSV file that is cut off part way through still gives you every record before the cut.