It really depends on what you are looking for.
DA:O is, as people said, fairly linear. It has a decent enough story, with pause/start action where you can choose tactics within your party. The voice acting is good, and the origin stories where you are playing through why you are in the world from a race stand point are fairly well done. Also, you can get this game very cheap by now I am assuming. With that said, it's sequel is horrible and if you would be hoping for any continuation of the story to make sense or tie in together, forget it. EA will kill what's left of this franchise.
Skyrim will be more open world sandbox obviously. The story in of itself is decent enough, but there is a lot to do in the world in terms of varying quest lines and you are not told where to go. You just go around and start doing things. The bonuses obviously is a ton of content from the mods. I have all three DLC so far. Dawnguard was fun, albeit a bit short and you will choose between two questlines. Heartfire is cheap, but VERY addicting. It's only 5 bucks. With Heartfire you will cut your own wood at various wood mills, which are then automatically transferred to your "house". You can build blue prints to add on and over time make a plethora of wings (Library, Enchating room, kitchen, bedrooms, etc) for lots of storage of your items. The lore is expansive. I have spent hours just cruising around gathering resources and adding things to my house and "living" in the world. It's pretty fun for $4.99. Dragonborn was one of the best expansion packs I have played with a very cool campaign and story line to it.
Graphically, Skyrim takes the cake but this will be subjective. Both are pretty enough games. It's really going to depend on the type of game you are looking for. I prefer open world these days, and have put over 100 hours into Skyrim. While putting about 25 into DA:O.
Price conerned: If you think Dragon Age Origin is more your cup of tea play style wise, you can get the ultimate edition with includes all the content packs and expansions now for $29.99. There is a 20% off coupon so you could get this for the low twenties and activate on steam. This deal is on Greenmangaming.com. If you choose Skyrim, you can get the full game now off sale for $39.99 on Steam, which would be better than what Green Man Gaming has it for with the coupon (Still selling for $49.99 there)
Overall, my recommendation would be Skyrim.
Edit: If you can wait it out a bit, Skyrim will most likely be getting a GOTY edition soon and will sell cheap on Steam. I would guess around this summer. If you cannot, look aroudn various places. I saw on Amazon you can get the DVD version for 24 bucks and if you are a prime member, that means 2 day shipping for free.