Berty,
I actually had one when they were first coming on the Neo scene, before !ARCADE! was selling the Phantom-1 converter, and yes, You DO get an options menu.
See, ALL NeoGeo MVS games were originally slated to be released on the Home Cart system, even though some like Ninja Masters, Super Dodgeball, and a few others that I cant recall never did make it home. What determines whether or not you get an options screen is the BIOS in the machine being used. You see, the hardware in the MVS carts and Home carts is IDENTICAL, except for some rewireing, and the ROM chips are connected to larger PCBs, hence the problem of MVS carts not fitting Home systems, and vice versa. But they are the exact same boards and information. So, when using a MVS converter to convert the arcade only release of "Super Dodge Ball" (yes, all home carts of SDB are CONVERSIONS, not real releases) you WILL get an options screen, with Difficulty, 2 Player Vs, etc. Just like a regular Home cart game. Same thing. Now, on the other end of the spectrum, if there WAS a converter for Home to MVS, (which there is NOT, it would be pointless) and you stuck the home version of Fatal Fury 3 in the converter, and powered up your MVS, it would NOT give you options, it would act just like the Arcade counterpart.
A good way to explain this is to use the Emulators. Sorry about the ROM talk Admins, but this actualy does answer his question. When you use an emulator, you can usually set the emu to work as an MVS, or a home system, yet you only have ONE set of ROMs, not 2, arcade and home. Thats because the actual program code in the games are identical, so when the MVS version of Game X was dumped, so was the Home Version.
Sorry im a bit wordy, but I hope that helps.