Asbestos tile removal is not too bad a job - you have to keep it damp and avoid skil sawing or sanding it (things that create dust), but not a tough DIY job or contractor job in most areas - though gets into the $1000-2000 for normal size room in the ecoalarmist states where it has been made out to be a major hazard, when it is not if used and handled properly.
I can't see taking up the subfloor is going to help unless the tile is bonded (like with true asphaltic mastic from the 60's and 7u0's, which REALLY holds on - though will succumb to heat, though a fire hazard in that case) so tight you can't take it up, in which case knife cutting through the tile along subfloor board joints to lift up as a unit is viable to only a limited extent - because usually the subfloor goes in under the walls (as well as cabinets sometimes if not taking them out), so you would have a perimeter cut to do all around. Can be done with a slow-moving wetted sawzall blade (being careful not to nick joists or utilities in the subfloor) but slow and somewhat expensive - so if the vinyl flooring will come up I would go that way for certain.
Also - if in an area where your landfill cannot take asbestos in the general fill, so it has to go to an expensive specialty hazardous waste facility or contractor, or where there is a much higher dump fee per pound for asbestos containing material, removing it with the subfloor is going to increase your dump fee by probably 5-10 fold if disposing of it with the plywood.
Here is a related previous question with answer which might help too:
https://answers.angieslist.com/What-f...
