"Better" might be a matter of interpretation. The oils will behave a bit differently, however.
Mineral Oil is a non-drying oil, which means that it will not polymerize (form a plastic-like substance) over time. This is good for oiling cutting boards because it will stay a bit liquid in the wood and flow into cracks and scratches. It is also food-safe and won't go rancid or support microorganisms.
Linseed Oil (AKA Flaxseed Oil, or Flax Oil) is also a good choice, for a different reason. Linseed Oil is a drying oil, which means it will fully polymerize and form a harder plastic layer. This is why it is about the best oil for seasoning cast iron pans. It may be more durable than mineral oil, but lacks the ability to "flow".
A blend of the two sounds like a fine idea. My favorite, Howard's Butcher Block Conditioner is a mix of Mineral Oil and natural waxes like Carnauba and Beeswax, which add a bit of that "durability" that Linseed Oil could add.
What would be a bad choice are most food oils like Canola, Olive Oil, Lard, etc. Unsaturated fats will oxidize (go rancid) and affect your food. Even oils high in saturated fats may have too many anti-oxidants (which are bad in this case), which will prevent polymerization and leave a gummy surface. These semi-drying oils are of no use here.
Whatever you use, make sure it is intended for food (Linseed Oil is a common woodworking finish, and not all versions are intended for use with food). Mineral Oil is probably more convenient for quick daily wipe-downs, while some of the blends are probably a bit more suited toward occasional re-finishing. Either way, regular application and keeping the board dry while not in use will make more difference than the exact type of oil.
Not much you can do about a warped wooden cutting board to be honest apart from either chuck it out or live with its warpedness! I do sympathise, I have a warped one too!
In future (I'm going to heed my own advice) use food grade wood oil on the wooden cutting board, this goes a long way to stopping it from warping, protecting the surface and making it easy to clean.
Best Answer
I wouldn't use that board any further. Some of those gaps where the block laminate is separating go right the way through. I don't see how you could realistically sanitise it, even if the other side looks a bit better.
Not only would I replace it, I'd also seriously consider replacing the counter top. The chipboard is swollen due to repeated wetting & is not going to be anything like hygienic any more. If you do consider only changing the chopping board, at least make sure the chipboard is properly sealed before you replace it, & consider mounting the new board with silicone sealant around the edges.
Perhaps this may not apply world-wide, but in the UK that style of square-edged countertop hasn't been in use for at least 30 years. Pretty much everything since then is bullnose or semi-bullnose (half-round or quarter-round) - meaning there is no separate mica piece on the front edge, it's all made in one continuous, watertight, piece.
In consequence that chipboard could have more than 30 years of contamination in it.