I've actually been through both of these! Over the holidays at my in-laws country place the pump that pushes the waste from the basement toilet up to the septic drain got jammed (kids - long story) and had to be removed, cleaned and put back in place. It was a messy/smelly job!
When I refinished my basement we had to move a toilet drain. We did just cap the old one. Ran a new line for the new position. Not that difficult, but quite physically demanding, loud and messy to break concrete. Cheap to do yourself (mostly labour) which is why I can see it would be quite expensive to contract it out depending on how the long the revised run is.
One other word of advice - make sure you know where the main electrical cables go. Another long story, but the short version is at another house where we were (yet again) moving the toilet location in the basement, we hit the main electrical line coming in for the house from the meter. Huge electrical fireball, thankfully nobody hurt, and very expensive to have the house put back on the grid again - only qualified electricians are allowed to deal with hooking up to the meter on the outside of the house!
