Either will work. If you run it under the pad, I would make the conduit larger than required, just in case. Add a pull string for future service.
If you are planning on a stub in the concrete to set the spa over, make sure your dimensions are accurate. This is where going external is an advantage as positioning is not as critical.
As for cost, are you capable of running the conduit and wire, mounting the spa panel and such or are you going to have to hire an electrician? DIY is going to run around $500-$750 or so depending on how far away from the main panel you are, the spa panel or disconnect and then if you need GFCI's in the main panel (if you decide on a disconnect instead of a spa panel) and the size wire needed. If you need cable, the best price on line I found is Nassau National Cable. They beat my local electrical supply house by a lot on wire.
I installed my electric for my spa. The cost was 60' of 6-3 romex for $150, 60A GFCI breaker was $90, disconnect was $15 and about $50 in conduit, clamps and sealtite fittings. I saved a bit because I was also running a dedicated service to my garage and had some large conduit already installed for my main panel that I could run the 6-3 in.
I would imagine that an electrician is going to run you $2000-$3000.